Stochastic numerics for mathematical physics:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
[2004]
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| Series: | Scientific computation
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IXX, 594 Seiten Illustrationen |
| ISBN: | 9783540211105 3540211101 |
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| 245 | 1 | 0 | |a Stochastic numerics for mathematical physics |c G. N. Milstein ; M. V. Tretyakov |
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Record in the Search Index
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| adam_text |
G. N. MILSTEIN M. V. TRETYAKOV STOCHASTIC NUMERICS FOR MATHEMATICAL
PHYSICS WITH 48 FIGURES AND 28 TABLES SPRINGER TABLE OF CONTENTS
MEAN-SQUARE APPROXIMATION FOR STOCHASTIC DIFFERENTIAL EQUATIONS 1 1.1
FUNDAMENTAL THEOREM ON THE MEAN-SQUARE ORDER OF CONVERGENCE 3 1.1.1
STATEMENT OF THE THEOREM 3 1.1.2 PROOF OF THE FUNDAMENTAL THEOREM 5
1.1.3 THE FUNDAMENTAL THEOREM FOR EQUATIONS IN THE SENSE OF STRATONOVICH
9 1.1.4 DISCUSSION 10 1.1.5 THE EXPLICIT EULER METHOD 12 1.1.6
NONGLOBALLY LIPSCHITZ CONDITIONS 16 1.2 METHODS BASED ON TAYLOR-TYPE
EXPANSION 18 1.2.1 TAYLOR EXPANSION OF SOLUTIONS OF ORDINARY
DIFFERENTIAL EQUATIONS 18 1.2.2 WAGNER-PLATEN EXPANSION OF SOLUTIONS OF
STOCHASTIC DIFFERENTIAL EQUATIONS 19 1.2.3 CONSTRUCTION OF EXPLICIT
METHODS 23 1.3 IMPLICIT MEAN-SQUARE METHODS 29 1.3.1 CONSTRUCTION OF
DRIFT-IMPLICIT METHODS 29 1.3.2 THE BALANCED METHOD 33 1.3.3 IMPLICIT
METHODS FOR SDES WITH LOCALLY LIPSCHITZ VECTOR FIELDS 37 1.3.4 FULLY
IMPLICIT MEAN-SQUARE METHODS: THE MAIN IDEA . . 38 1.3.5 CONVERGENCE
THEOREM FOR FULLY IMPLICIT METHODS 41 1.3.6 GENERAL CONSTRUCTION OF
FULLY IMPLICIT METHODS 43 1.4 MODELING OF ITO INTEGRALS 45 1.4.1 ITO
INTEGRALS DEPENDING ON A SINGLE NOISE AND METHODS OF ORDER 3/2 AND 2 45
1.4.2 MODELING ITO INTEGRALS BY THE RECTANGLE AND TRAPEZIUM METHODS 51
1.4.3 MODELING ITO INTEGRALS BY THE FOURIER METHOD 54 1.5 EXPLICIT AND
IMPLICIT METHODS OF ORDER 3/2 FOR SYSTEMS WITH ADDITIVE NOISE 60 1.5.1
EXPLICIT METHODS BASED ON TAYLOR-TYPE EXPANSION 60 1.5.2 IMPLICIT
METHODS BASED ON TAYLOR-TYPE EXPANSION 62 X TABLE OF CONTENTS 1.5.3
STIFF SYSTEMS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE.
YL-STABILITY 66 1.5.4 RUNGE-KUTTA TYPE METHODS 71 1.5.5 TWO-STEP
DIFFERENCE METHODS 75 1.6 NUMERICAL SCHEMES FOR EQUATIONS WITH COLORED
NOISE 77 1.6.1 EXPLICIT SCHEMES OF ORDERS 2 AND 5/2 78 1.6.2 RUNGE-KUTTA
SCHEMES 80 1.6.3 IMPLICIT SCHEMES 81 2 WEAK APPROXIMATION FOR STOCHASTIC
DIFFERENTIAL EQUATIONS 83 2.1 ONE-STEP APPROXIMATION 87 2.1.1 PROPERTIES
OF REMAINDERS AND ITO INTEGRALS 88 2.1.2 ONE-STEP APPROXIMATIONS OF
THIRD ORDER 92 2.1.3 THE TAYLOR EXPANSION OF MATHEMATICAL EXPECTATIONS .
. 98 2.2 THE MAIN THEOREM ON CONVERGENCE OF WEAK APPROXIMATIONS AND
METHODS OF ORDER TWO 99 2.2.1 THE GENERAL CONVERGENCE THEOREM 100 2.2.2
RUNGE-KUTTA TYPE METHODS 104 2.2.3 THE TALAY-TUBARO EXTRAPOLATION METHOD
105 2.2.4 IMPLICIT METHOD 109 2.3 WEAK METHODS FOR SYSTEMS WITH ADDITIVE
AND COLORED NOISE. 112 2.3.1 SECOND-ORDER METHODS 113 2.3.2 MAIN
LEMMAS FOR THIRD-ORDER METHODS 113 2.3.3 CONSTRUCTION OF A METHOD OF
ORDER THREE 116 2.3.4 WEAK SCHEMES FOR SYSTEMS WITH COLORED NOISE 121
2.4 VARIANCE REDUCTION 123 2.4.1 THE METHOD OF IMPORTANT SAMPLING . .
.' 123 2.4.2 VARIANCE REDUCTION BY CONTROL VARIATES AND COMBINING
METHOD 126 2.4.3 VARIANCE REDUCTION FOR BOUNDARY VALUE PROBLEMS 129 2.5
APPLICATION OF WEAK METHODS TO THE MONTE CARLO COMPUTATION OF WIENER
INTEGRALS 130 2.5.1 THE TRAPEZIUM, RECTANGLE, AND OTHER METHODS OF
SECOND ORDER 133, 2.5.2 A FOURTH-ORDER RUNGE-KUTTA METHOD FOR COMPUTING
WIENER INTEGRALS OF FUNCTIONALS OF EXPONENTIAL TYPE. 135 2.5.3
EXPLICIT RUNGE-KUTTA METHOD OF ORDER FOUR FOR CONDITIONAL WIENER
INTEGRALS OF EXPONENTIAL-TYPE FUNCTIONALS 137 2.5.4 THEOREM ON ONE-STEP
ERROR 140 2.5.5 IMPLICIT RUNGE-KUTTA METHODS FOR CONDITIONAL WIENER
INTEGRALS OF EXPONENTIAL-TYPE FUNCTIONALS 145 2.5.6 NUMERICAL
EXPERIMENTS 148 2.6 RANDOM NUMBER GENERATORS 159 TABLE OF CONTENTS XI
2.6.1 SOME UNIFORM RANDOM NUMBER GENERATORS 160 2.6.2 A SPECIFIC TEST
FOR SDE INTEGRATION 163 2.6.3 GENERATION OF GAUSSIAN RANDOM NUMBERS 166
2.6.4 PARALLEL IMPLEMENTATION 168 3 NUMERICAL METHODS FOR SDES WITH
SMALL NOISE 171 3.1 MEAN-SQUARE APPROXIMATIONS AND ESTIMATION OF THEIR
ERRORS . . 173 3.1.1 CONSTRUCTION OF ONE-STEP MEAN-SQUARE APPROXIMATION
. 173 3.1.2 THEOREM ON MEAN-SQUARE GLOBAL ESTIMATE 175 3.1.3 SELECTION
OF TIME INCREMENT H DEPENDING ON PARAMETER E 177 3.1.4 (H, E)-APPROACH
VERSUS (E, /I)-APPROACH 177 3.2 SOME CONCRETE MEAN-SQUARE METHODS FOR
SYSTEMS WITH SMALL NOISE 178 3.2.1 TAYLOR-TYPE NUMERICAL METHODS 179
3.2.2 RUNGE-KUTTA METHODS 180 3.2.3 IMPLICIT METHODS 182 3.2.4
STRATONOVICH SDES WITH SMALL NOISE 183 3.2.5 MEAN-SQUARE METHODS FOR
SYSTEMS WITH SMALL ADDITIVE NOISE 184 3.3 NUMERICAL TESTS OF MEAN-SQUARE
METHODS 185 3.3.1 SIMULATION OF LYAPUNOV EXPONENT OF A LINEAR SYSTEM
WITH SMALL NOISE 185 3.3.2 STOCHASTIC MODEL OF A LASER 188 3.4 THE MAIN
THEOREM ON ERROR ESTIMATION AND GENERAL APPROACH TO CONSTRUCTION OF WEAK
METHODS 190 3.5 SOME CONCRETE WEAK METHODS 193 3.5.1 TAYLOR-TYPE METHODS
193 3.5.2 RUNGE-KUTTA METHODS 196 3.5.3 WEAK METHODS FOR SYSTEMS WITH
SMALL ADDITIVE NOISE . . 199 3.6 EXPANSION OF THE GLOBAL ERROR IN POWERS
OF H AND E 202 3.7 REDUCTION OF THE MONTE CARLO ERROR 203 3.8 SIMULATION
OF THE LYAPUNOV EXPONENT OF A LINEAR SYSTEM WITH SMALL NOISE BY WEAK
METHODS 206 4 STOCHASTIC HAMILTONIAN SYSTEMS AND LANGEVIN-TYPE EQUATIONS
211 4.1 PRESERVATION OF SYMPLECTIC STRUCTURE 213 4.2 MEAN-SQUARE
SYMPLECTIC METHODS FOR STOCHASTIC HAMILTONIAN SYSTEMS 216 4.2.1 GENERAL
STOCHASTIC HAMILTONIAN SYSTEMS 216 4.2.2 EXPLICIT METHODS IN THE CASE OF
SEPARABLE HAMILTONIANS 220 4.3 MEAN-SQUARE SYMPLECTIC METHODS FOR
HAMILTONIAN SYSTEMS WITH ADDITIVE NOISE 224 4.3.1 THE CASE OF A GENERAL
HAMILTONIAN 224 4.3.2 THE CASE OF SEPARABLE HAMILTONIANS 231 XII TABLE
OF CONTENTS 4.3.3 THE CASE OF HAMILTONIAN H(T,P,Q) = L -P T M^ V +U{T,Q)
234 4.4 NUMERICAL TESTS OF MEAN-SQUARE SYMPLECTIC METHODS 237 4.4.1 KUBO
OSCILLATOR 237 4.4.2 A MODEL FOR SYNCHROTRON OSCILLATIONS OF PARTICLES
IN STORAGE RINGS 239 4.4.3 LINEAR OSCILLATOR WITH ADDITIVE NOISE 240 4.5
LIOUVILLIAN METHODS FOR STOCHASTIC SYSTEMS PRESERVING PHASE VOLUME 246
4.5.1 LIOUVILLIAN METHODS FOR PARTITIONED SYSTEMS WITH MULTIPLICAETIVE
NOISE 248 4.5.2 LIOUVILLIAN METHODS FOR A VOLUME-PRESERVING SYSTEM WITH
ADDITIVE NOISE 250 4.6 WEAK SYMPLECTIC METHODS FOR STOCHASTIC
HAMILTONIAN SYSTEMS 251 4.6.1 HAMILTONIAN SYSTEMS WITH MULTIPLICAETIVE
NOISE 251 4.6.2 HAMILTONIAN SYSTEMS WITH ADDITIVE NOISE 255 4.6.3
NUMERICAL TESTS 257 4.7 QUASI-SYMPLECTIC MEAN-SQUARE METHODS FOR
LANGEVIN-TYPE EQUATIONS 261 4.7.1 LANGEVIN EQUATION: LINEAR DAMPING AND
ADDITIVE NOISE 262 4.7.2 LANGEVIN-TYPE EQUATION: NONLINEAR DAMPING AND
MULTIPLICAETIVE NOISE 270 4.8 QUASI-SYMPLECTIC WEAK METHODS FOR
LANGEVIN-TYPE EQUATIONS . 273 4.8.1 LANGEVIN EQUATION: LINEAR DAMPING
AND ADDITIVE NOISE 273 4.8.2 LANGEVIN-TYPE EQUATION: NONLINEAR DAMPING
AND MULTIPLICAETIVE NOISE 275 4.8.3 NUMERICAL EXAMPLES 276 SIMULATION OF
SPACE AND SPACE-TIME BOUNDED DIFFUSIONS . . 283 5.1 MEAN-SQUARE
APPROXIMATION FOR AUTONOMOUS SDES WITHOUT DRIFT IN A SPACE BOUNDED
DOMAIN 286 5.1.1 LOCAL APPROXIMATION OF DIFFUSION IN A SPACE BOUNDED
DOMAIN 287 5.1.2 GLOBAL ALGORITHM FOR DIFFUSION IN A SPACE BOUNDED
DOMAIN 291 5.1.3 SIMULATION OF EXIT POINT X X (T X ) 301 5.2 SYSTEMS
WITH DRIFT IN A SPACE BOUNDED DOMAIN 302 5.3 SPACE-TIME BROWNIAN MOTION
306 5.3.1 AUXILIARY KNOWLEDGE 306 5.3.2 SOME DISTRIBUTIONS FOR
ONE-DIMENSIONAL WIENER PROCESS 308 5.3.3 SIMULATION OF EXIT TIME AND
EXIT POINT OF WIENER PROCESS FROM A CUBE 313 5.3.4 SIMULATION OF EXIT
POINT OF THE SPACE-TIME BROWNIAN MOTION FROM A SPACE-TIME PARALLELEPIPED
WITH CUBIC BASE 316 TABLE OF CONTENTS XIII 5.4 APPROXIMATIONS FOR SDES
IN A SPACE-TIME BOUNDED DOMAIN . 317 5.4.1 LOCAL MEAN-SQUARE
APPROXIMATION IN A SPACE-TIME BOUNDED DOMAIN 318 5.4.2 GLOBAL ALGORITHM
IN A SPACE-TIME BOUNDED DOMAIN . 322 5.4.3 APPROXIMATION OF EXIT
POINT (R, X(T)) 325 5.4.4 SIMULATION OF SPACE-TIME BROWNIAN MOTION WITH
DRIFT . 328 5.5 NUMERICAL EXAMPLES 329 5.6 MEAN-SQUARE APPROXIMATION OF
DIFFUSION WITH REFLECTION 337 RANDOM WALKS FOR LINEAR BOUNDARY VALUE
PROBLEMS 339 6.1 ALGORITHMS FOR SOLVING THE DIRICHLET PROBLEM BASED ON
TIME-STEP CONTROL 339 6.1.1 THEOREMS ON ONE-STEP APPROXIMATION 341 6.1.2
NUMERICAL ALGORITHMS AND CONVERGENCE THEOREMS 348 6.2 THE SIMPLEST
RANDOM WALK FOR THE DIRICHLET PROBLEM FOR PARABOLIC EQUATIONS 353 6.2.1
THE ALGORITHM OF THE SIMPLEST RANDOM WALK 353 6.2.2 CONVERGENCE THEOREM
356 6.2.3 OTHER RANDOM WALKS 359 6.2.4 NUMERICAL TESTS 364 6.3 RANDOM
WALKS FOR THE ELLIPTIC DIRICHLET PROBLEM 365 6.3.1 THE SIMPLEST RANDOM
WALK FOR ELLIPTIC EQUATIONS 366 6.3.2 OTHER METHODS FOR ELLIPTIC
PROBLEMS 370 6.3.3 NUMERICAL TESTS 372 6.4 SPECIFIC RANDOM WALKS FOR
ELLIPTIC EQUATIONS AND BOUNDARY LAYER 374 6.4.1 CONDITIONAL EXPECTATION
OF ITO INTEGRALS CONNECTED WITH WIENER PROCESS IN THE BALL 376 6.4.2
SPECIFIC ONE-STEP APPROXIMATIONS FOR ELLIPTIC EQUATIONS . 380 6.4.3 THE
AVERAGE NUMBER OF STEPS 384 6.4.4 NUMERICAL ALGORITHMS AND CONVERGENCE
THEOREMS 388 6.5 METHODS FOR ELLIPTIC EQUATIONS WITH SMALL PARAMETER AT
HIGHER DERIVATIVES 392 6.6 METHODS FOR THE NEUMANN PROBLEM FOR PARABOLIC
EQUATIONS . . 397 6.6.1 ONE-STEP APPROXIMATION FOR BOUNDARY POINTS . 399
6.6.2 CONVERGENCE THEOREMS 403 PROBABILISTIC APPROACH TO NUMERICAL
SOLUTION OF THE CAUCHY PROBLEM FOR NONLINEAR PARABOLIC EQUATIONS . . 407
7.1 PROBABILISTIC APPROACH TO LINEAR PARABOLIC EQUATIONS 408 7.2 LAYER
METHODS FOR SEMILINEAR PARABOLIC EQUATIONS 415 7.2.1 THE CONSTRUCTION OF
LAYER METHODS 415 7.2.2 CONVERGENCE THEOREM FOR A LAYER METHOD 419 7.2.3
NUMERICAL ALGORITHMS 422 7.3 MULTI-DIMENSIONAL CASE 427 XIV TABLE OF
CONTENTS 7.3.1 MULTIDIMENSIONAL PARABOLIC EQUATION 427 7.3.2
PROBABILISTIC APPROACH TO REACTION-DIFFUSION SYSTEMS . . . 429 7.4
NUMERICAL EXAMPLES 431 7.5 PROBABILISTIC APPROACH TO SEMILINEAR
PARABOLIC EQUATIONS WITH SMALL PARAMETER 438 7.5.1 IMPLICIT LAYER METHOD
AND ITS CONVERGENCE 440 7.5.2 EXPLICIT LAYER METHODS 442 7.5.3 SINGULAR
CASE 443 7.5.4 NUMERICAL ALGORITHMS BASED ON INTERPOLATION 445 7.6
HIGH-ORDER METHODS FOR SEMILINEAR EQUATION WITH SMALL CONSTANT DIFFUSION
AND ZERO ADVECTION 446 7.6.1 TWO-LAYER METHODS 447 7.6.2 THREE-LAYER
METHODS 448 7.7 NUMERICAL TESTS ' 451 7.7.1 THE BURGERS EQUATION WITH
SMALL VISCOSITY 452 7.7.2 THE GENERALIZED FKPP-EQUATION WITH A SMALL
PARAMETER 455 8 NUMERICAL SOLUTION OF THE NONLINEAR DIRICHLET AND
NEUMANN PROBLEMS BASED ON THE PROBABILISTIC APPROACH . . 461 8.1 LAYER
METHODS FOR THE DIRICHLET PROBLEM FOR SEMILINEAR PARABOLIC EQUATIONS 461
8.1.1 CONSTRUCTION OF A LAYER METHOD OF FIRST ORDER 463 8.1.2
CONVERGENCE THEOREM 467 8.1.3 A LAYER METHOD WITH A SIMPLER
APPROXIMATION NEAR THE BOUNDARY 468 8.1.4 NUMERICAL ALGORITHMS AND THEIR
CONVERGENCE 474 8.2 EXTENSION TO THE MULTI-DIMENSIONAL DIRICHLET PROBLEM
476 8.3 NUMERICAL TESTS OF LAYER METHODS FOR THE DIRICHLET PROBLEMS . .
479 8.3.1 THE BURGERS EQUATION 479 8.3.2 COMPARISON ANALYSIS 482 8.3.3
QUASILINEAR EQUATION WITH POWER LAW NONLINEARITIES . . . 485 8.4 LAYER
METHODS FOR THE NEUMANN PROBLEM FOR SEMILINEAR PARABOLIC EQUATIONS 488
8.4.1 CONSTRUCTION OF LAYER METHODS 489 8.4.2 CONVERGENCE THEOREMS 493
8.4.3 NUMERICAL ALGORITHMS 497 8.4.4 SOME OTHER LAYER METHODS 499 8.5
EXTENSION TO THE MULTI-DIMENSIONAL NEUMANN PROBLEM 501 8.6 NUMERICAL
TESTS FOR THE NEUMANN PROBLEM 503 8.6.1 COMPARISON OF VARIOUS LAYER
METHODS 503 8.6.2 A COMPARISON ANALYSIS OF LAYER METHODS AND
FINITE-DIFFERENCE SCHEMES 505 TABLE OF CONTENTS XV 9 APPLICATION OF
STOCHASTIC NUMERICS TO MODEIS WITH STOCHASTIC RESONANCE AND TO BROWNIAN
RATCHETS . 509 9.1 NOISE-INDUCED REGULAER OSCILLATIONS IN SYSTEMS WITH
STOCHASTIC RESONANCE 510 9.1.1 SUFFICIENT CONDITIONS FOR REGULAER
OSCILLATIONS 512 9.1.2 COMPARISON WITH THE APPROACH BASED ON KRAMERS'
THEORY OF DIFFUSION OVER A POTENTIAL BARRIER 517 9.1.3 HIGH-FREQUENCY
REGULAER OSCILLATIONS IN SYSTEMS WITH MULTIPLICAETIVE NOISE 518 9.1.4
LARGE-AMPLITUDE REGULAER OSCILLATIONS IN MONOSTABLE SYSTEM 523 9.1.5
REGULAER OSCILLATIONS IN A SYSTEM OF TWO COUPLED OSCILLATORS 525 9.2
NOISE-INDUCED UNIDIRECTIONAL TRANSPORT 526 9.2.1 SYSTEMS WITH
STATE-DEPENDENT DIFFUSION 528 9.2.2 FORCED THERMAL RATCHETS 533 A
APPENDIX: PRACTICAL GUIDANCE TO IMPLEMENTATION OF THE STOCHASTIC
NUMERICAL METHODS 541 A.L MEAN-SQUARE METHODS 541 A.2 WEAK METHODS AND
THE MONTE CARLO TECHNIQUE 544 A.3 ALGORITHMS FOR BOUNDED DIFFUSIONS 550
A.4 RANDOM WALKS FOR LINEAR BOUNDARY VALUE PROBLEMS 558 A.5 NONLINEAR
PDES 560 A.6 MISCELLANEOUS 565 REFERENCES 571 INDEX 587 |
| any_adam_object | 1 |
| author | Milʹstejn, Grigorij N. 1937- Tretʹjakov, Michail V. |
| author_GND | (DE-588)12144371X (DE-588)1055733566 |
| author_facet | Milʹstejn, Grigorij N. 1937- Tretʹjakov, Michail V. |
| author_role | aut aut |
| author_sort | Milʹstejn, Grigorij N. 1937- |
| author_variant | g n m gn gnm m v t mv mvt |
| building | Verbundindex |
| bvnumber | BV019425202 |
| classification_rvk | SK 820 SK 950 |
| ctrlnum | (OCoLC)633809981 (DE-599)BVBBV019425202 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV019425202 |
| illustrated | Illustrated |
| indexdate | 2024-09-20T04:22:46Z |
| institution | BVB |
| isbn | 9783540211105 3540211101 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012886775 |
| oclc_num | 633809981 |
| open_access_boolean | |
| owner | DE-573 DE-20 DE-384 DE-29T DE-739 DE-634 DE-11 DE-188 DE-83 |
| owner_facet | DE-573 DE-20 DE-384 DE-29T DE-739 DE-634 DE-11 DE-188 DE-83 |
| physical | IXX, 594 Seiten Illustrationen |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Scientific computation |
| spelling | Milʹstejn, Grigorij N. 1937- (DE-588)12144371X aut Stochastic numerics for mathematical physics G. N. Milstein ; M. V. Tretyakov Berlin [u.a.] Springer [2004] © 2004 IXX, 594 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Scientific computation Probabilistischer Algorithmus (DE-588)4504622-0 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Stochastische Differentialgleichung (DE-588)4057621-8 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Probabilistischer Algorithmus (DE-588)4504622-0 s Tretʹjakov, Michail V. (DE-588)1055733566 aut Erscheint auch als Online-Ausgabe 978-3-662-10063-9 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012886775&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Milʹstejn, Grigorij N. 1937- Tretʹjakov, Michail V. Stochastic numerics for mathematical physics Probabilistischer Algorithmus (DE-588)4504622-0 gnd Mathematische Physik (DE-588)4037952-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4504622-0 (DE-588)4037952-8 (DE-588)4128130-5 (DE-588)4057621-8 |
| title | Stochastic numerics for mathematical physics |
| title_auth | Stochastic numerics for mathematical physics |
| title_exact_search | Stochastic numerics for mathematical physics |
| title_full | Stochastic numerics for mathematical physics G. N. Milstein ; M. V. Tretyakov |
| title_fullStr | Stochastic numerics for mathematical physics G. N. Milstein ; M. V. Tretyakov |
| title_full_unstemmed | Stochastic numerics for mathematical physics G. N. Milstein ; M. V. Tretyakov |
| title_short | Stochastic numerics for mathematical physics |
| title_sort | stochastic numerics for mathematical physics |
| topic | Probabilistischer Algorithmus (DE-588)4504622-0 gnd Mathematische Physik (DE-588)4037952-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Probabilistischer Algorithmus Mathematische Physik Numerisches Verfahren Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012886775&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT milʹstejngrigorijn stochasticnumericsformathematicalphysics AT tretʹjakovmichailv stochasticnumericsformathematicalphysics |