Verfügbarkeit: Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations:

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Butcher, John C. 1933- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Chichester [u.a.] Wiley 2008
Ausgabe:	2. ed.
Schlagworte:	Numerisches Verfahren Gewöhnliche Differentialgleichung Konferenzschrift > 1991 > Dublin
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIX, 463 S. Ill., graph. Darst.
ISBN:	9780470723357

Internformat

MARC


LEADER	00000nam a2200000zc 4500
001	BV023219727
003	DE-604
005	20111206
007	t
008	080318s2008 xxuad\|\| \|\|\|\| 00\|\|\| eng d
020			\|a 9780470723357 \|9 978-0-470-72335-7
035			\|a (OCoLC)635178047
035			\|a (DE-599)BVBBV023219727
040			\|a DE-604 \|b ger \|e aacr
041	0		\|a eng
044			\|a xxu \|c US
049			\|a DE-355 \|a DE-703 \|a DE-29T \|a DE-634 \|a DE-11 \|a DE-20 \|a DE-824 \|a DE-19 \|a DE-898 \|a DE-1050 \|a DE-83
084			\|a SK 500 \|0 (DE-625)143243: \|2 rvk
084			\|a SK 520 \|0 (DE-625)143244: \|2 rvk
084			\|a SK 920 \|0 (DE-625)143272: \|2 rvk
084			\|a 65L06 \|2 msc
084			\|a 65L05 \|2 msc
084			\|a 65L20 \|2 msc
084			\|a 34A12 \|2 msc
100	1		\|a Butcher, John C. \|d 1933- \|e Verfasser \|0 (DE-588)13615638X \|4 aut
245	1	0	\|a Numerical methods for ordinary differential equations \|c J. C. Butcher
250			\|a 2. ed.
264		1	\|a Chichester [u.a.] \|b Wiley \|c 2008
300			\|a XIX, 463 S. \|b Ill., graph. Darst.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
650	0	7	\|a Numerisches Verfahren \|0 (DE-588)4128130-5 \|2 gnd \|9 rswk-swf
650	0	7	\|a Gewöhnliche Differentialgleichung \|0 (DE-588)4020929-5 \|2 gnd \|9 rswk-swf
655		7	\|8 1\p \|0 (DE-588)1071861417 \|a Konferenzschrift \|y 1991 \|z Dublin \|2 gnd-content
689	0	0	\|a Gewöhnliche Differentialgleichung \|0 (DE-588)4020929-5 \|D s
689	0	1	\|a Numerisches Verfahren \|0 (DE-588)4128130-5 \|D s
689	0		\|5 DE-604
856	4	2	\|m Digitalisierung UB Regensburg \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-016405658
883	1		\|8 1\p \|a cgwrk \|d 20201028 \|q DE-101 \|u https://d-nb.info/provenance/plan#cgwrk

Datensatz im Suchindex

_version_	1804137506373894144
adam_text	Contents Preface to the first edition .................... xiii Preface to the second edition .................. xvii 1 Differential and Difference Equations .......... 1 10 Differential Equation Problems ............... 1 100 Introduction to differential equations ........... І 101 The Kepler problem .................... 4 102 A problem arising from the method of lines ....... 7 103 The simple pendulum .................... 10 10Ą A chemical kinetics problem ................ 14 105 The Van der Pol equation and limit cycles ........ 16 106 The Lotka-Volterra problem and periodic orbits ..... 18 107 The Euler equations of rigid body rotation ........ 20 11 Differential Equation Theory ................. 22 110 Existence and uniqueness of solutions .......... 22 111 Linear systems of differential equations ......... 24 112 Stiff differential equations ................. 26 12 Further Evolutionary Problems ............... 28 120 Many-body gravitational problems ............. 28 121 Delay problems and discontinuous solutions ....... 31 122 Problems evolving on a sphere ............... 32 123 Further Hamiltonian problems ............... 34 124 Further differential-algebraic problems .......... 36 13 Difference Equation Problems ................ 38 130 Introduction to difference equations ............ 38 131 Ä linear problem ...................... 38 132 The Fibonacci difference equation ............. 40 133 Three quadratic problems ................. 40 ISA Iterative solutions of a polynomial equation ....... 41 135 The arithmetic-geometric mean .............. 43 CONTENTS 14 Difference Equation Theory .................. 44 IAO Linear difference equations ................ 44 1Ą1 Constant coefficients .................... 45 1Ą2 Powers of matrices ..................... 46 Numerical Differential Equation Methods ....... 51 20 The Euler Method ........................ 51 200 Introduction to the Euler methods ............. 51 201 Some numerical experiments ............... 54 202 Calculations with stepsize control ............. 58 203 Calculations with mildly stiff problems .......... 60 204 Calculations with the implicit Euler method ....... 63 21 Analysis of the Euler Method ................ 65 210 Formulation of the Euler method ............. 65 211 Local truncation error ................... 66 212 Global truncation error ................... 66 213 Convergence of the Euler method ............. 68 214 Order of convergence .................... 69 215 Asymptotic error formula ................. 72 216 Stability characteristics .................. 74 211 Local truncation error estimation ............. 79 218 Rounding error ....................... 80 22 Generalizations of the Euler Method ............ 85 220 Introduction ......................... 85 221 More computations in a step ............... 86 222 Greater dependence on previous values .......... 87 223 Use of higher derivatives .................. 88 22Ą Multistep-multistage-multiderivative methods ...... 90 225 Implicit methods ...................... 91 226 Local error estimates .................... 91 23 Runge-Kutta Methods ..................... 93 230 Historical introduction ................... 93 231 Second order methods ................... 93 232 The coefficient tableau ................... 94 233 Third order methods .................... 95 234 Introduction to order conditions .............. 95 235 Fourth order methods ................... 98 236 Higher orders ........................ 99 237 Implicit Runge-Kutta methods .............. 99 238 Stability characteristics .................. 100 Numerical examples .................... 103 CONTENTS vii 24 Linear Multistep Methods................... 105 24O Historical introduction ................... 105 BAI Adams methods ....................... 105 242 General form of linear multistep methods ........ 107 243 Consistency, stability and convergence .......... 107 244 Predictor-corrector Adams methods ............ 109 245 The Milne device ...................... Ill 246 Starting methods ...................... 112 247 Numerical examples .................... 113 25 Taylor Series Methods ..................... 114 250 Introduction to Taylor series methods .......... 114 251 Manipulation of power series ............... 115 252 An example of a Taylor series solution .......... 116 253 Other methods using higher derivatives .......... 119 254 The use of f derivatives .................. 120 255 Further numerical examples ................ 121 26 Hybrid Methods ......................... 122 260 Historical introduction ................... 122 261 Pseudo Runge-Kutta methods ............... 123 262 Generalized linear multistep methods ........... 124 263 General linear methods ................... 124 264 Numerical examples .................... 127 27 Introduction to Implementation ............... 128 270 Choice of method ...................... 128 271 Variable stepsize ...................... 130 272 Interpolation ........................ 131 273 Experiments with the Kepler problem ........... 132 274 Experiments with a discontinuous problem ........ 133 3 Runge-Kutta Methods ..................... 137 30 Preliminaries ........................... 137 300 Rooted trees ......................... 137 301 Functions on trees ..................... 139 302 Some combinatorial questions ............... 141 303 The use of labelled trees .................. 144 304 Enumerating non-rooted trees ............... 144 305 Differentiation ....................... 146 306 Taylor s theorem ...................... 148 31 Order Conditions ........................ 150 310 Elementary differentials .................. 150 311 The Taylor expansion of the exact solution ....... 153 312 Elementary weights ..................... 155 313 The Taylor expansion of the approximate solution .... 159 314 Independence of the elementary differentials ....... 160 315 Conditions for order .................... 162 CONTENTS 316 Order conditions for scalar problems ...........162 317 Independence, of elementary weights ...........163 318 Local truncation error ...................165 319 Global truncation error ...................166 32 Low Order Explicit Methods .................170 320 Methods of orders less than 4...............170 321 Simplifying assumptions ..................171 322 Methods of order 4.....................175 323 New methods from old ...................181 324 Order barriers .......................187 325 Methods of order 5.....................190 326 Methods of order 6.....................192 327 Methods of orders greater than 6.............195 33 Runge-Kutta Methods with Error Estimates ......198 330 Introduction .........................198 331 Richardson error estimates ................198 332 Methods with built-in estimates ..............201 333 A class of error-estimating methods ...........202 334 The methods of Fehlberg..................208 335 The methods of Verner ...................210 336 The methods of Dormand and Prince ...........211 34 Implicit Runge-Kutta Methods ...............213 340 Introduction .........................213 341 Solvability of implicit equations ..............214 342 Methods based on Gaussian quadrature ..........215 343 Reflected methods ......................219 344 Methods based on Radau and Lobatto quadrature .... 222 35 Stability of Implicit Runge-Kutta Methods .......230 350 A-stability ; А(ог)- stability and L-stability .........230 351 Criteria for A-stability ...................230 352 Padé approximations to the exponential function .... 232 353 A-stability of Gauss and related methods ........238 354 Order stars .........................240 355 Order arrows and the Ehle barrier ............243 356 AN-stability .........................245 357 Non-linear stability .....................248 358 BN-stability of collocation methods ............252 359 The V and W transformations ..............254 36 Implementable Implicit Runge— Kutta Methods .....259 360 Implementation of implicit Runge-Kutta methods .... 259 361 Diagonally implicit Runge-Kutta methods ........261 362 The importance of high stage order ............262 363 Singly implicit methods ..................266 364 Generalizations of singly implicit methods ........271 365 Effective order and DESIRE methods ...........273 CONTENTS ix 37 Symplectic Runge-Kutta Methods .............275 370 Maintaining quadratic invariants .............275 371 Examples of symplectic methods ..............276 372 Order conditions ......................277 573 Experiments with symplectic methods ...........278 38 Algebraic Properties of Runge-Kutta Methods .....280 380 Motivation .........................280 381 Equivalence classes of Runge-Kutta methods ......281 382 The group of Runge-Kutta methods ............284 383 The Runge-Kutta group ..................287 384 A homomorphism between two groups ..........290 385 A generalization of G% ...................291 386 Recursive formula for the product .............292 387 Some special elements of G ................297 388 Some subgroups and quotient groups ...........300 389 An algebraic interpretation of effective order .......302 39 Implementation Issues .....................308 390 Introduction .........................308 391 Optimal sequences .....................308 392 Acceptance and rejection of steps .............310 393 Error per step versus error per unit step .........311 394 Control-theoretic considerations ..............312 395 Solving the implicit equations ...............313 4 Linear Multistep Methods ..................317 40 Preliminaries ...........................317 400 Fundamentals ........................317 401 Starting methods ......................318 402 Convergence .........................319 403 Stability ...........................320 404 Consistency .........................320 405 Necessity of conditions for convergence ..........322 406 Sufficiency of conditions for convergence .........324 41 The Order of Linear Multistep Methods ..........329 410 Criteria f or order ......................329 411 Derivation of methods ...................330 Ą12 Backward difference methods ...............332 42 Errors and Error Growth ...................333 420 Introduction .........................333 421 Further remarks on error growth .............335 422 The underlying one-step method .............337 423 Weakly stable methods ...................339 Ą2Ą Variable stepsize ......................340 ; CONTENTS 43 Stability Characteristics ....................342 430 Introduction .........................342 431 Stability regions .......................344 432 Examples of the boundary locus method .........346 433 An example of the Schur criterion ............349 434 Stability of predictor-corrector methods .........349 44 Order and Stability Barriers .................352 440 Survey of barrier results ..................352 441 Maximum order for a convergent k-step method .....353 44^ Order stars for linear multistep methods .........356 44З Order arrows for linear multistep methods ........358 45 One-Leg Methods and G-stability ..............360 450 The one-leg counterpart to a linear multistep method . . 360 451 The concept of G-stability .................361 452 Transformations relating one-leg and linear multistep methods ...........................364 453 Effective order interpretation ...............365 454 Concluding remarks on G-stability ............365 46 Implementation Issues .....................366 460 Survey of implementation considerations .........366 461 Representation of data ...................367 462 Variable stepsize for Nordsieck methods .........371 463 Local error estimation ...................372 5 General Linear Methods ....................373 50 Representing Methods in General Linear Form .....373 500 Multivalue-multistage methods ..............373 501 Transformations of methods ................375 502 Runge-Kutta methods as general linear methods .....376 503 Linear multistep methods as general linear methods . . . 377 504 Some known unconventional methods ...........380 505 Some recently discovered general linear methods .....382 51 Consistency, Stability and Convergence ..........385 510 Definitions of consistency and stability ..........385 511 Govariance of methods ...................386 512 Definition of convergence .................387 513 The necessity of stability .................388 514 The necessity of consistency ................389 515 Stability and consistency imply convergence .......390 52 The Stability of General Linear Methods .........397 520 Introduction .........................397 521 Methods with maximal stability order ...........398 522 Outline proof of the Butcher- Chipman conjecture . . . 402 523 Non-linear stability .....................405 524 Reducible linear multistep methods and G-stability . . . 407 525 G-symplectic methods ...................408 CONTENTS xi 53 The Order of General Linear Methods........... 410 530 Possible definitions of order ................410 531 Local and global truncation errors .............412 532 Algebraic analysis of order .................413 533 An example of the algebraic approach to order ......414 53Ą The order of a G-symplectic method ...........416 535 The underlying one-step method .............417 54 Methods with Runge-Kutta stability ............420 ОАО Design criteria for general linear methods ........420 541 The types of DIMSIM methods ..............420 542 Runge-Kutta stability ...................423 543 Almost Runge-Kutta methods ...............426 544 Third order, three-stage ARK methods ..........429 545 Fourth order, four-stage ARK methods ..........431 546 A fifth order, five-stage method ..............433 547 ARK methods for stiff problems ..............434 55 Methods with Inherent Runge—Kutta Stability .....436 550 Doubly companion matrices ................436 551 Inherent Runge-Kutta stability ..............438 552 Conditions for zero spectral radius ............440 553 Derivation of methods with IRK stability .........442 554 Methods with property F ..................445 555 Some non-stiff methods ..................446 556 Some stiff methods .....................447 557 Scale and modify for stability ...............448 558 Scale and modify for error estimation ..........450 References ................................453 Index ....................................459
adam_txt	Contents Preface to the first edition . xiii Preface to the second edition . xvii 1 Differential and Difference Equations . 1 10 Differential Equation Problems . 1 100 Introduction to differential equations . І 101 The Kepler problem . 4 102 A problem arising from the method of lines . 7 103 The simple pendulum . 10 10Ą A chemical kinetics problem . 14 105 The Van der Pol equation and limit cycles . 16 106 The Lotka-Volterra problem and periodic orbits . 18 107 The Euler equations of rigid body rotation . 20 11 Differential Equation Theory . 22 110 Existence and uniqueness of solutions . 22 111 Linear systems of differential equations . 24 112 Stiff differential equations . 26 12 Further Evolutionary Problems . 28 120 Many-body gravitational problems . 28 121 Delay problems and discontinuous solutions . 31 122 Problems evolving on a sphere . 32 123 Further Hamiltonian problems . 34 124 Further differential-algebraic problems . 36 13 Difference Equation Problems . 38 130 Introduction to difference equations . 38 131 Ä linear problem . 38 132 The Fibonacci difference equation . 40 133 Three quadratic problems . 40 ISA Iterative solutions of a polynomial equation . 41 135 The arithmetic-geometric mean . 43 CONTENTS 14 Difference Equation Theory . 44 IAO Linear difference equations . 44 1Ą1 Constant coefficients . 45 1Ą2 Powers of matrices . 46 Numerical Differential Equation Methods . 51 20 The Euler Method . 51 200 Introduction to the Euler methods . 51 201 Some numerical experiments . 54 202 Calculations with stepsize control . 58 203 Calculations with mildly stiff problems . 60 204 Calculations with the implicit Euler method . 63 21 Analysis of the Euler Method . 65 210 Formulation of the Euler method . 65 211 Local truncation error . 66 212 Global truncation error . 66 213 Convergence of the Euler method . 68 214 Order of convergence . 69 215 Asymptotic error formula . 72 216 Stability characteristics . 74 211 Local truncation error estimation . 79 218 Rounding error . 80 22 Generalizations of the Euler Method . 85 220 Introduction . 85 221 More computations in a step . 86 222 Greater dependence on previous values . 87 223 Use of higher derivatives . 88 22Ą Multistep-multistage-multiderivative methods . 90 225 Implicit methods . 91 226 Local error estimates . 91 23 Runge-Kutta Methods . 93 230 Historical introduction . 93 231 Second order methods . 93 232 The coefficient tableau . 94 233 Third order methods . 95 234 Introduction to order conditions . 95 235 Fourth order methods . 98 236 Higher orders . 99 237 Implicit Runge-Kutta methods . 99 238 Stability characteristics . 100 Numerical examples . 103 CONTENTS vii 24 Linear Multistep Methods. 105 24O Historical introduction . 105 BAI Adams methods . 105 242 General form of linear multistep methods . 107 243 Consistency, stability and convergence . 107 244 Predictor-corrector Adams methods . 109 245 The Milne device . Ill 246 Starting methods . 112 247 Numerical examples . 113 25 Taylor Series Methods . 114 250 Introduction to Taylor series methods . 114 251 Manipulation of power series . 115 252 An example of a Taylor series solution . 116 253 Other methods using higher derivatives . 119 254 The use of f derivatives . 120 255 Further numerical examples . 121 26 Hybrid Methods . 122 260 Historical introduction . 122 261 Pseudo Runge-Kutta methods . 123 262 Generalized linear multistep methods . 124 263 General linear methods . 124 264 Numerical examples . 127 27 Introduction to Implementation . 128 270 Choice of method . 128 271 Variable stepsize . 130 272 Interpolation . 131 273 Experiments with the Kepler problem . 132 274 Experiments with a discontinuous problem . 133 3 Runge-Kutta Methods . 137 30 Preliminaries . 137 300 Rooted trees . 137 301 Functions on trees . 139 302 Some combinatorial questions . 141 303 The use of labelled trees . 144 304 Enumerating non-rooted trees . 144 305 Differentiation . 146 306 Taylor's theorem . 148 31 Order Conditions . 150 310 Elementary differentials . 150 311 The Taylor expansion of the exact solution . 153 312 Elementary weights . 155 313 The Taylor expansion of the approximate solution . 159 314 Independence of the elementary differentials . 160 315 Conditions for order . 162 CONTENTS 316 Order conditions for scalar problems .162 317 Independence, of elementary weights .163 318 Local truncation error .165 319 Global truncation error .166 32 Low Order Explicit Methods .170 320 Methods of orders less than 4.170 321 Simplifying assumptions .171 322 Methods of order 4.175 323 New methods from old .181 324 Order barriers .187 325 Methods of order 5.190 326 Methods of order 6.192 327 Methods of orders greater than 6.195 33 Runge-Kutta Methods with Error Estimates .198 330 Introduction .198 331 Richardson error estimates .198 332 Methods with built-in estimates .201 333 A class of error-estimating methods .202 334 The methods of Fehlberg.208 335 The methods of Verner .210 336 The methods of Dormand and Prince .211 34 Implicit Runge-Kutta Methods .213 340 Introduction .213 341 Solvability of implicit equations .214 342 Methods based on Gaussian quadrature .215 343 Reflected methods .219 344 Methods based on Radau and Lobatto quadrature . 222 35 Stability of Implicit Runge-Kutta Methods .230 350 A-stability ; А(ог)- stability and L-stability .230 351 Criteria for A-stability .230 352 Padé approximations to the exponential function . 232 353 A-stability of Gauss and related methods .238 354 Order stars .240 355 Order arrows and the Ehle barrier .243 356 AN-stability .245 357 Non-linear stability .248 358 BN-stability of collocation methods .252 359 The V and W transformations .254 36 Implementable Implicit Runge— Kutta Methods .259 360 Implementation of implicit Runge-Kutta methods . 259 361 Diagonally implicit Runge-Kutta methods .261 362 The importance of high stage order .262 363 Singly implicit methods .266 364 Generalizations of singly implicit methods .271 365 Effective order and DESIRE methods .273 CONTENTS ix 37 Symplectic Runge-Kutta Methods .275 370 Maintaining quadratic invariants .275 371 Examples of symplectic methods .276 372 Order conditions .277 573 Experiments with symplectic methods .278 38 Algebraic Properties of Runge-Kutta Methods .280 380 Motivation .280 381 Equivalence classes of Runge-Kutta methods .281 382 The group of Runge-Kutta methods .284 383 The Runge-Kutta group .287 384 A homomorphism between two groups .290 385 A generalization of G% .291 386 Recursive formula for the product .292 387 Some special elements of G .297 388 Some subgroups and quotient groups .300 389 An algebraic interpretation of effective order .302 39 Implementation Issues .308 390 Introduction .308 391 Optimal sequences .308 392 Acceptance and rejection of steps .310 393 Error per step versus error per unit step .311 394 Control-theoretic considerations .312 395 Solving the implicit equations .313 4 Linear Multistep Methods .317 40 Preliminaries .317 400 Fundamentals .317 401 Starting methods .318 402 Convergence .319 403 Stability .320 404 Consistency .320 405 Necessity of conditions for convergence .322 406 Sufficiency of conditions for convergence .324 41 The Order of Linear Multistep Methods .329 410 Criteria f or order .329 411 Derivation of methods .330 Ą12 Backward difference methods .332 42 Errors and Error Growth .333 420 Introduction .333 421 Further remarks on error growth .335 422 The underlying one-step method .337 423 Weakly stable methods .339 Ą2Ą Variable stepsize .340 ; CONTENTS 43 Stability Characteristics .342 430 Introduction .342 431 Stability regions .344 432 Examples of the boundary locus method .346 433 An example of the Schur criterion .349 434 Stability of'predictor-corrector methods .349 44 Order and Stability Barriers .352 440 Survey of barrier results .352 441 Maximum order for a convergent k-step method .353 44^ Order stars for linear multistep methods .356 44З Order arrows for linear multistep methods .358 45 One-Leg Methods and G-stability .360 450 The one-leg counterpart to a linear multistep method . . 360 451 The concept of G-stability .361 452 Transformations relating one-leg and linear multistep methods .364 453 Effective order interpretation .365 454 Concluding remarks on G-stability .365 46 Implementation Issues .366 460 Survey of implementation considerations .366 461 Representation of data .367 462 Variable stepsize for Nordsieck methods .371 463 Local error estimation .372 5 General Linear Methods .373 50 Representing Methods in General Linear Form .373 500 Multivalue-multistage methods .373 501 Transformations of methods .375 502 Runge-Kutta methods as general linear methods .376 503 Linear multistep methods as general linear methods . . . 377 504 Some known unconventional methods .380 505 Some recently discovered general linear methods .382 51 Consistency, Stability and Convergence .385 510 Definitions of consistency and stability .385 511 Govariance of methods .386 512 Definition of convergence .387 513 The necessity of stability .388 514 The necessity of consistency .389 515 Stability and consistency imply convergence .390 52 The Stability of General Linear Methods .397 520 Introduction .397 521 Methods with maximal stability order .398 522 Outline proof of the Butcher- Chipman conjecture . . . 402 523 Non-linear stability .405 524 Reducible linear multistep methods and G-stability . . . 407 525 G-symplectic methods .408 CONTENTS xi 53 The Order of General Linear Methods. 410 530 Possible definitions of order .410 531 Local and global truncation errors .412 532 Algebraic analysis of order .413 533 An example of the algebraic approach to order .414 53Ą The order of a G-symplectic method .416 535 The underlying one-step method .417 54 Methods with Runge-Kutta stability .420 ОАО Design criteria for general linear methods .420 541 The types of DIMSIM methods .420 542 Runge-Kutta stability .423 543 Almost Runge-Kutta methods .426 544 Third order, three-stage ARK methods .429 545 Fourth order, four-stage ARK methods .431 546 A fifth order, five-stage method .433 547 ARK methods for stiff problems .434 55 Methods with Inherent Runge—Kutta Stability .436 550 Doubly companion matrices .436 551 Inherent Runge-Kutta stability .438 552 Conditions for zero spectral radius .440 553 Derivation of methods with IRK stability .442 554 Methods with property F .445 555 Some non-stiff methods .446 556 Some stiff methods .447 557 Scale and modify for stability .448 558 Scale and modify for error estimation .450 References .453 Index .459
any_adam_object	1
any_adam_object_boolean	1
author	Butcher, John C. 1933-
author_GND	(DE-588)13615638X
author_facet	Butcher, John C. 1933-
author_role	aut
author_sort	Butcher, John C. 1933-
author_variant	j c b jc jcb
building	Verbundindex
bvnumber	BV023219727
classification_rvk	SK 500 SK 520 SK 920
ctrlnum	(OCoLC)635178047 (DE-599)BVBBV023219727
discipline	Mathematik
discipline_str_mv	Mathematik
edition	2. ed.
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01870nam a2200457zc 4500</leader><controlfield tag="001">BV023219727</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20111206 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080318s2008 xxuad\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780470723357</subfield><subfield code="9">978-0-470-72335-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)635178047</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023219727</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-1050</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 500</subfield><subfield code="0">(DE-625)143243:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 920</subfield><subfield code="0">(DE-625)143272:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65L06</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65L05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65L20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">34A12</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Butcher, John C.</subfield><subfield code="d">1933-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)13615638X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical methods for ordinary differential equations</subfield><subfield code="c">J. C. Butcher</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Chichester [u.a.]</subfield><subfield code="b">Wiley</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 463 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4020929-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="y">1991</subfield><subfield code="z">Dublin</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4020929-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016405658</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection>
genre	1\p (DE-588)1071861417 Konferenzschrift 1991 Dublin gnd-content
genre_facet	Konferenzschrift 1991 Dublin
id	DE-604.BV023219727
illustrated	Illustrated
index_date	2024-07-02T20:15:29Z
indexdate	2024-07-09T21:13:23Z
institution	BVB
isbn	9780470723357
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016405658
oclc_num	635178047
open_access_boolean
owner	DE-355 DE-BY-UBR DE-703 DE-29T DE-634 DE-11 DE-20 DE-824 DE-19 DE-BY-UBM DE-898 DE-BY-UBR DE-1050 DE-83
owner_facet	DE-355 DE-BY-UBR DE-703 DE-29T DE-634 DE-11 DE-20 DE-824 DE-19 DE-BY-UBM DE-898 DE-BY-UBR DE-1050 DE-83
physical	XIX, 463 S. Ill., graph. Darst.
publishDate	2008
publishDateSearch	2008
publishDateSort	2008
publisher	Wiley
record_format	marc
spelling	Butcher, John C. 1933- Verfasser (DE-588)13615638X aut Numerical methods for ordinary differential equations J. C. Butcher 2. ed. Chichester [u.a.] Wiley 2008 XIX, 463 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1991 Dublin gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Butcher, John C. 1933- Numerical methods for ordinary differential equations Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd
subject_GND	(DE-588)4128130-5 (DE-588)4020929-5 (DE-588)1071861417
title	Numerical methods for ordinary differential equations
title_auth	Numerical methods for ordinary differential equations
title_exact_search	Numerical methods for ordinary differential equations
title_exact_search_txtP	Numerical methods for ordinary differential equations
title_full	Numerical methods for ordinary differential equations J. C. Butcher
title_fullStr	Numerical methods for ordinary differential equations J. C. Butcher
title_full_unstemmed	Numerical methods for ordinary differential equations J. C. Butcher
title_short	Numerical methods for ordinary differential equations
title_sort	numerical methods for ordinary differential equations
topic	Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd
topic_facet	Numerisches Verfahren Gewöhnliche Differentialgleichung Konferenzschrift 1991 Dublin
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016405658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT butcherjohnc numericalmethodsforordinarydifferentialequations

Verfügbarkeit

Es ist kein Print-Exemplar vorhanden.

Fernleihe Bestellen Achtung: Nicht im THWS-Bestand! Inhaltsverzeichnis

MARC

Datensatz im Suchindex

Es ist kein Print-Exemplar vorhanden.

Ähnliche Einträge