The numerical solution of ordinary and partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, N.J.
John Wiley
2005
|
| Edition: | 2. ed. |
| Series: | Pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 333 S. graph. Darst. |
| ISBN: | 0471735809 9780471735809 |
Staff View
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Record in the Search Index
| _version_ | 1804134581850341376 |
|---|---|
| adam_text | THE NUMERICAL SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
SECOND EDITION GRANVILLE SEWELL TEXAS A&M UNIVERSITY MATHEMATICS
DEPARTMENT COLLEGE STATION, TEXAS AND UNIVERSITY OF TEXAS-EL PASO EL
PASO, TEXAS IWILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS PREFACE XI DIRECT SOLUTION OF LINEAR SYSTEMS 1 0.0 INTRODUCTION
1 0.1 GENERAL LINEAR SYSTEMS 1 0.2 SYSTEMS REQUIRING NO PIVOTING 5 0.3
THE LU DECOMPOSITION 8 0.4 BANDED LINEAR SYSTEMS 11 0.5 SPARSE DIRECT
METHODS 17 0.6 PROBLEMS 24 INITIAL VALUE ORDINARY DIFFERENTIAL EQUATIONS
27 1.0 INTRODUCTION 27 1.1 EULER S METHOD 28 1.2 TRUNCATION ERROR,
STABILITY, AND CONVERGENCE 30 1.3 MULTISTEP METHODS 35 1.4 ADAMS
MULTISTEP METHODS 39 1.5 BACKWARD DIFFERENCE METHODS FOR STIFF PROBLEMS
46 1.6 RUNGE-KUTTA METHODS 51 1.7 PROBLEMS 58 THE INITIAL VALUE
DIFFUSION PROBLEM 62 2.0 INTRODUCTION 62 2.1 AN EXPLICIT METHOD 65 2.2
IMPLICIT METHODS 70 2.3 A ONE-DIMENSIONAL EXAMPLE 74 2.4
MULTIDIMENSIONAL PROBLEMS 77 2.5 A DIFFUSION-REACTION EXAMPLE 83 2.6
PROBLEMS 86 THE INITIAL VALUE TRANSPORT AND WAVE PROBLEMS 91 3.0
INTRODUCTION 91 3.1 EXPLICIT METHODS FOR THE TRANSPORT PROBLEM 97 VII
VIII CONTENTS 3.2 THE METHOD OF CHARACTERISTICS 103 3.3 AN EXPLICIT
METHOD FOR THE WAVE EQUATION 108 3.4 A DAMPED WAVE EXAMPLE 113 3.5
PROBLEMS 116 4 BOUNDARY VALUE PROBLEMS 120 4.0 INTRODUCTION 120 4.1
FINITE DIFFERENCE METHODS 123 4.2 A NONLINEAR EXAMPLE 125 4.3 A SINGULAR
EXAMPLE 127 4.4 SHOOTING METHODS 129 4.5 MULTIDIMENSIONAL PROBLEMS 133
4.6 SUCCESSIVE OVERRELAXATION 137 4.7 SUCCESSIVE OVERRELAXATION EXAMPLES
140 4.8 THE CONJUGATE-GRADIENT METHOD 150 4.9 SYSTEMS OF DIFFERENTIAL
EQUATIONS 156 4.10 THE EIGENVALUE PROBLEM 160 4.11 THE INVERSE POWER
METHOD 164 4.12 PROBLEMS 168 5 THE FINITE ELEMENT METHOD 174 5.0
INTRODUCTION 174 5.1 THE GALERKIN METHOD 174 5.2 EXAMPLE USING PIECE
WISE LINEAR TRIAL FUNCTIONS 179 5.3 EXAMPLE USING CUBIC HERMITE TRIAL
FUNCTIONS 182 5.4 A SINGULAR EXAMPLE AND THE COLLOCATION METHOD 192 5.5
LINEAR TRIANGULAR ELEMENTS 199 5.6 AN EXAMPLE USING TRIANGULAR ELEMENTS
202 5.7 TIME-DEPENDENT PROBLEMS 206 5.8 A ONE-DIMENSIONAL EXAMPLE 209
5.9 TIME-DEPENDENT EXAMPLE USING TRIANGLES 213 5.10 THE EIGENVALUE
PROBLEM 217 5.11 EIGENVALUE EXAMPLES 219 5.12 PROBLEMS 227 APPENDIX A -
SOLVING PDES WITH PDE2D 235 A.I HISTORY 235 A.2 THE PDE2D INTERACTIVE
USER INTERFACE 236 A.3 ONE-DIMENSIONAL STEADY-STATE PROBLEMS 239 A.4
TWO-DIMENSIONAL STEADY-STATE PROBLEMS 241 A.5 THREE-DIMENSIONAL
STEADY-STATE PROBLEMS 248 A.6 NONRECTANGULAR 3D REGIONS 251 A.7
TIME-DEPENDENT PROBLEMS 258 A.8 EIGENVALUE PROBLEMS 261 A.9 THE PDE2D
PARALLEL LINEAR SYSTEM SOLVERS 262 CONTENTS IX A.10 EXAMPLES 268 A.LL
PROBLEMS 275 APPENDIX B - THE FOURIER STABILITY METHOD 282 APPENDIX C -
MATLAB PROGRAMS 288 APPENDIX D - CAN ANYTHING HAPPEN IN AN OPEN
SYSTEM? 316 APPENDIX E - ANSWERS TO SELECTED EXERCISES 320 REFERENCES
327 INDEX 331
|
| adam_txt |
THE NUMERICAL SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
SECOND EDITION GRANVILLE SEWELL TEXAS A&M UNIVERSITY MATHEMATICS
DEPARTMENT COLLEGE STATION, TEXAS AND UNIVERSITY OF TEXAS-EL PASO EL
PASO, TEXAS IWILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS PREFACE XI DIRECT SOLUTION OF LINEAR SYSTEMS 1 0.0 INTRODUCTION
1 0.1 GENERAL LINEAR SYSTEMS 1 0.2 SYSTEMS REQUIRING NO PIVOTING 5 0.3
THE LU DECOMPOSITION 8 0.4 BANDED LINEAR SYSTEMS 11 0.5 SPARSE DIRECT
METHODS 17 0.6 PROBLEMS 24 INITIAL VALUE ORDINARY DIFFERENTIAL EQUATIONS
27 1.0 INTRODUCTION 27 1.1 EULER'S METHOD 28 1.2 TRUNCATION ERROR,
STABILITY, AND CONVERGENCE 30 1.3 MULTISTEP METHODS 35 1.4 ADAMS
MULTISTEP METHODS 39 1.5 BACKWARD DIFFERENCE METHODS FOR STIFF PROBLEMS
46 1.6 RUNGE-KUTTA METHODS 51 1.7 PROBLEMS 58 THE INITIAL VALUE
DIFFUSION PROBLEM 62 2.0 INTRODUCTION 62 2.1 AN EXPLICIT METHOD 65 2.2
IMPLICIT METHODS 70 2.3 A ONE-DIMENSIONAL EXAMPLE 74 2.4
MULTIDIMENSIONAL PROBLEMS 77 2.5 A DIFFUSION-REACTION EXAMPLE 83 2.6
PROBLEMS 86 THE INITIAL VALUE TRANSPORT AND WAVE PROBLEMS 91 3.0
INTRODUCTION 91 3.1 EXPLICIT METHODS FOR THE TRANSPORT PROBLEM 97 VII
VIII CONTENTS 3.2 THE METHOD OF CHARACTERISTICS 103 3.3 AN EXPLICIT
METHOD FOR THE WAVE EQUATION 108 3.4 A DAMPED WAVE EXAMPLE 113 3.5
PROBLEMS 116 4 BOUNDARY VALUE PROBLEMS 120 4.0 INTRODUCTION 120 4.1
FINITE DIFFERENCE METHODS 123 4.2 A NONLINEAR EXAMPLE 125 4.3 A SINGULAR
EXAMPLE 127 4.4 SHOOTING METHODS 129 4.5 MULTIDIMENSIONAL PROBLEMS 133
4.6 SUCCESSIVE OVERRELAXATION 137 4.7 SUCCESSIVE OVERRELAXATION EXAMPLES
140 4.8 THE CONJUGATE-GRADIENT METHOD 150 4.9 SYSTEMS OF DIFFERENTIAL
EQUATIONS 156 4.10 THE EIGENVALUE PROBLEM 160 4.11 THE INVERSE POWER
METHOD 164 4.12 PROBLEMS 168 5 THE FINITE ELEMENT METHOD 174 5.0
INTRODUCTION 174 5.1 THE GALERKIN METHOD 174 5.2 EXAMPLE USING PIECE
WISE LINEAR TRIAL FUNCTIONS 179 5.3 EXAMPLE USING CUBIC HERMITE TRIAL
FUNCTIONS 182 5.4 A SINGULAR EXAMPLE AND THE COLLOCATION METHOD 192 5.5
LINEAR TRIANGULAR ELEMENTS 199 5.6 AN EXAMPLE USING TRIANGULAR ELEMENTS
202 5.7 TIME-DEPENDENT PROBLEMS 206 5.8 A ONE-DIMENSIONAL EXAMPLE 209
5.9 TIME-DEPENDENT EXAMPLE USING TRIANGLES 213 5.10 THE EIGENVALUE
PROBLEM 217 5.11 EIGENVALUE EXAMPLES 219 5.12 PROBLEMS 227 APPENDIX A -
SOLVING PDES WITH PDE2D 235 A.I HISTORY 235 A.2 THE PDE2D INTERACTIVE
USER INTERFACE 236 A.3 ONE-DIMENSIONAL STEADY-STATE PROBLEMS 239 A.4
TWO-DIMENSIONAL STEADY-STATE PROBLEMS 241 A.5 THREE-DIMENSIONAL
STEADY-STATE PROBLEMS 248 A.6 NONRECTANGULAR 3D REGIONS 251 A.7
TIME-DEPENDENT PROBLEMS 258 A.8 EIGENVALUE PROBLEMS 261 A.9 THE PDE2D
PARALLEL LINEAR SYSTEM SOLVERS 262 CONTENTS IX A.10 EXAMPLES 268 A.LL
PROBLEMS 275 APPENDIX B - THE FOURIER STABILITY METHOD 282 APPENDIX C -
MATLAB PROGRAMS 288 APPENDIX D - CAN "ANYTHING" HAPPEN IN AN OPEN
SYSTEM? 316 APPENDIX E - ANSWERS TO SELECTED EXERCISES 320 REFERENCES
327 INDEX 331 |
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| discipline | Mathematik |
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| id | DE-604.BV020861661 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:23:13Z |
| indexdate | 2024-07-09T20:26:54Z |
| institution | BVB |
| isbn | 0471735809 9780471735809 |
| language | English |
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| physical | XII, 333 S. graph. Darst. |
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| publisher | John Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spelling | Sewell, Granville 1948- Verfasser (DE-588)1080329455 aut The numerical solution of ordinary and partial differential equations Granville Sewell 2. ed. Hoboken, N.J. John Wiley 2005 XII, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Partiële differentiaalvergelijkingen gtt Datenverarbeitung Differential equations Numerical solutions Data processing Differential equations, Partial Numerical solutions Data processing Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Datenverarbeitung (DE-588)4011152-0 s Differentialgleichung (DE-588)4012249-9 s Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014183203&sequence=000001&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 | Sewell, Granville 1948- The numerical solution of ordinary and partial differential equations Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Partiële differentiaalvergelijkingen gtt Datenverarbeitung Differential equations Numerical solutions Data processing Differential equations, Partial Numerical solutions Data processing Datenverarbeitung (DE-588)4011152-0 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4011152-0 (DE-588)4020929-5 (DE-588)4012249-9 (DE-588)4042805-9 (DE-588)4128130-5 (DE-588)4044779-0 |
| title | The numerical solution of ordinary and partial differential equations |
| title_auth | The numerical solution of ordinary and partial differential equations |
| title_exact_search | The numerical solution of ordinary and partial differential equations |
| title_exact_search_txtP | The numerical solution of ordinary and partial differential equations |
| title_full | The numerical solution of ordinary and partial differential equations Granville Sewell |
| title_fullStr | The numerical solution of ordinary and partial differential equations Granville Sewell |
| title_full_unstemmed | The numerical solution of ordinary and partial differential equations Granville Sewell |
| title_short | The numerical solution of ordinary and partial differential equations |
| title_sort | the numerical solution of ordinary and partial differential equations |
| topic | Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Partiële differentiaalvergelijkingen gtt Datenverarbeitung Differential equations Numerical solutions Data processing Differential equations, Partial Numerical solutions Data processing Datenverarbeitung (DE-588)4011152-0 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Gewone differentiaalvergelijkingen Numerieke methoden Partiële differentiaalvergelijkingen Datenverarbeitung Differential equations Numerical solutions Data processing Differential equations, Partial Numerical solutions Data processing Gewöhnliche Differentialgleichung Differentialgleichung Numerische Mathematik Numerisches Verfahren Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014183203&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sewellgranville thenumericalsolutionofordinaryandpartialdifferentialequations |