Numerical solution of partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Cambridge University Press
2005
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 278 S. graph. Darst. |
| ISBN: | 0521607930 9780521607933 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804134545987993600 |
|---|---|
| adam_text | NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS AN INTRODUCTION K.
W. MORTON UNIVERSITY OF BATH, UK AND D. F. MAYERS UNIVERSITY OF OXFORD,
UK SECOND EDITION CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE TO THE
FIRST EDITION PAGE VIII PREFACE TO THE SECOND EDITION XI 1 INTRODUCTION
1 2 PARABOLIC EQUATIONS IN ONE SPACE VARIABLE 7 2.1 INTRODUCTION 7 2.2 A
MODEL PROBLEM 7 2.3 SERIES APPROXIMATION 9 2.4 AN EXPLICIT SCHEME FOR
THE MODEL PROBLEM 10 2.5 DIFFERENCE NOTATION AND TRUNCATION ERROR 12 2.6
CONVERGENCE OF THE EXPLICIT SCHEME 16 2.7 FOURIER ANALYSIS OF THE ERROR
19 2.8 AN IMPLICIT METHOD 22 2.9 THE THOMAS ALGORITHM 24 2.10 THE
WEIGHTED AVERAGE OR ^-METHOD 26 2.11 A MAXIMUM PRINCIPLE AND CONVERGENCE
FOR /I(L -0) 33 2.12 A THREE-TIME-LEVEL SCHEME 38 2.13 MORE GENERAL
BOUNDARY CONDITIONS 39 2.14 HEAT CONSERVATION PROPERTIES 44 2.15 MORE
GENERAL LINEAR PROBLEMS 46 2.16 POLAR CO-ORDINATES 52 2.17 NONLINEAR
PROBLEMS 54 BIBLIOGRAPHIC NOTES 56 EXERCISES 56 VI CONTENTS 3 2-D AND
3-D PARABOLIC EQUATIONS 62 3.1 THE EXPLICIT METHOD IN A RECTILINEAR BOX
62 3.2 AN ADI METHOD IN TWO DIMENSIONS 64 3.3 ADI AND LOD METHODS IN
THREE DIMENSIONS 70 3.4 CURVED BOUNDARIES 71 3.5 APPLICATION TO GENERAL
PARABOLIC PROBLEMS 80 BIBLIOGRAPHIC NOTES 83 EXERCISES 83 4 HYPERBOLIC
EQUATIONS IN ONE SPACE DIMENSION 86 4.1 CHARACTERISTICS 86 4.2 THE CFL
CONDITION 89 4.3 ERROR ANALYSIS OF THE UPWIND SCHEME 94 4.4 FOURIER
ANALYSIS OF THE UPWIND SCHEME 97 4.5 THE LAX-WENDROFF SCHEME 100 4.6 THE
LAX*WENDROFF METHOD FOR CONSERVATION LAWS 103 4.7 FINITE VOLUME SCHEMES
110 4.8 THE BOX SCHEME 116 4.9 THE LEAP-FROG SCHEME 123 4.10 HAMILTONIAN
SYSTEMS AND SYMPLECTIC INTEGRATION SCHEMES 128 4.11 COMPARISON OF PHASE
AND AMPLITUDE ERRORS 135 4.12 BOVMDARY CONDITIONS AND CONSERVATION
PROPERTIES 139 4.13 EXTENSIONS TO MORE SPACE DIMENSIONS 143
BIBLIOGRAPHIC NOTES 146 EXERCISES 146 5 CONSISTENCY, CONVERGENCE AND
STABILITY 151 5.1 DEFINITION OF THE PROBLEMS CONSIDERED 151 5.2 THE
FINITE DIFFERENCE MESH AND NORMS 152 5.3 FINITE DIFFERENCE
APPROXIMATIONS 154 5.4 CONSISTENCY, ORDER OF ACCURACY AND CONVERGENCE
156 5.5 STABILITY AND THE LAX EQUIVALENCE THEOREM 157 5.6 CALCULATING
STABILITY CONDITIONS 160 5.7 PRACTICAL (STRICT OR STRONG) STABILITY 166
5.8 MODIFIED EQUATION ANALYSIS 169 5.9 CONSERVATION LAWS AND THE ENERGY
METHOD OF ANALYSIS 177 5.10 SUMMARY OF THE THEORY 186 BIBLIOGRAPHIC
NOTES 189 EXERCISES 190 CONTENTS VII 6 LINEAR SECOND ORDER ELLIPTIC
EQUATIONS IN TWO DIMENSIONS 194 6.1 A MODEL PROBLEM 194 6.2 ERROR
ANALYSIS OF THE MODEL PROBLEM 195 6.3 THE GENERAL DIFFUSION EQUATION 197
6.4 BOUNDARY CONDITIONS ON A CURVED BOUNDARY 199 6.5 ERROR ANALYSIS
USING A MAXIMUM PRINCIPLE 203 6.6 ASYMPTOTIC ERROR ESTIMATES 213 6.7
VARIATIONAL FORMULATION AND THE FINITE ELEMENT METHOD 218 6.8
CONVECTION-DIFFUSION PROBLEMS 224 6.9 AN EXAMPLE V 228 BIBLIOGRAPHIC
NOTES 231 EXERCISES 232 7 ITERATIVE SOLUTION OF LINEAR ALGEBRAIC
EQUATIONS 235 7.1 BASIC ITERATIVE SCHEMES IN EXPLICIT FORM 237 7.2
MATRIX FORM OF ITERATION METHODS AND THEIR CONVERGENCE 239 7.3 FOURIER
ANALYSIS OF CONVERGENCE 244 7.4 APPLICATION TO AN EXAMPLE 248 7.5
EXTENSIONS AND RELATED ITERATIVE METHODS 250 7.6 THE MULTIGRID METHOD
252 7.7 THE CONJUGATE GRADIENT METHOD 258 7.8 A NUMERICAL EXAMPLE:
COMPARISONS 261 BIBLIOGRAPHIC NOTES 263 EXERCISES 263 REFERENCES 267
INDEX 273
|
| adam_txt |
NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS AN INTRODUCTION K.
W. MORTON UNIVERSITY OF BATH, UK AND D. F. MAYERS UNIVERSITY OF OXFORD,
UK SECOND EDITION CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE TO THE
FIRST EDITION PAGE VIII PREFACE TO THE SECOND EDITION XI 1 INTRODUCTION
1 2 PARABOLIC EQUATIONS IN ONE SPACE VARIABLE 7 2.1 INTRODUCTION 7 2.2 A
MODEL PROBLEM 7 2.3 SERIES APPROXIMATION 9 2.4 AN EXPLICIT SCHEME FOR
THE MODEL PROBLEM 10 2.5 DIFFERENCE NOTATION AND TRUNCATION ERROR 12 2.6
CONVERGENCE OF THE EXPLICIT SCHEME 16 2.7 FOURIER ANALYSIS OF THE ERROR
19 2.8 AN IMPLICIT METHOD 22 2.9 THE THOMAS ALGORITHM 24 2.10 THE
WEIGHTED AVERAGE OR ^-METHOD 26 2.11 A MAXIMUM PRINCIPLE AND CONVERGENCE
FOR /I(L -0) \ 33 2.12 A THREE-TIME-LEVEL SCHEME 38 2.13 MORE GENERAL
BOUNDARY CONDITIONS 39 2.14 HEAT CONSERVATION PROPERTIES 44 2.15 MORE
GENERAL LINEAR PROBLEMS 46 2.16 POLAR CO-ORDINATES 52 2.17 NONLINEAR
PROBLEMS 54 BIBLIOGRAPHIC NOTES 56 EXERCISES 56 VI CONTENTS 3 2-D AND
3-D PARABOLIC EQUATIONS 62 3.1 THE EXPLICIT METHOD IN A RECTILINEAR BOX
62 3.2 AN ADI METHOD IN TWO DIMENSIONS 64 3.3 ADI AND LOD METHODS IN
THREE DIMENSIONS 70 3.4 CURVED BOUNDARIES 71 3.5 APPLICATION TO GENERAL
PARABOLIC PROBLEMS 80 BIBLIOGRAPHIC NOTES 83 EXERCISES 83 4 HYPERBOLIC
EQUATIONS IN ONE SPACE DIMENSION 86 4.1 CHARACTERISTICS 86 4.2 THE CFL
CONDITION 89 4.3 ERROR ANALYSIS OF THE UPWIND SCHEME 94 4.4 FOURIER
ANALYSIS OF THE UPWIND SCHEME 97 4.5 THE LAX-WENDROFF SCHEME 100 4.6 THE
LAX*WENDROFF METHOD FOR CONSERVATION LAWS 103 4.7 FINITE VOLUME SCHEMES
110 4.8 THE BOX SCHEME 116 4.9 THE LEAP-FROG SCHEME 123 4.10 HAMILTONIAN
SYSTEMS AND SYMPLECTIC INTEGRATION SCHEMES 128 4.11 COMPARISON OF PHASE
AND AMPLITUDE ERRORS 135 4.12 BOVMDARY CONDITIONS AND CONSERVATION
PROPERTIES 139 4.13 EXTENSIONS TO MORE SPACE DIMENSIONS 143
BIBLIOGRAPHIC NOTES 146 EXERCISES 146 5 CONSISTENCY, CONVERGENCE AND
STABILITY 151 5.1 DEFINITION OF THE PROBLEMS CONSIDERED 151 5.2 THE
FINITE DIFFERENCE MESH AND NORMS 152 5.3 FINITE DIFFERENCE
APPROXIMATIONS 154 5.4 CONSISTENCY, ORDER OF ACCURACY AND CONVERGENCE
156 5.5 STABILITY AND THE LAX EQUIVALENCE THEOREM 157 5.6 CALCULATING
STABILITY CONDITIONS 160 5.7 PRACTICAL (STRICT OR STRONG) STABILITY 166
5.8 MODIFIED EQUATION ANALYSIS 169 5.9 CONSERVATION LAWS AND THE ENERGY
METHOD OF ANALYSIS 177 5.10 SUMMARY OF THE THEORY 186 BIBLIOGRAPHIC
NOTES 189 EXERCISES 190 CONTENTS VII 6 LINEAR SECOND ORDER ELLIPTIC
EQUATIONS IN TWO DIMENSIONS 194 6.1 A MODEL PROBLEM 194 6.2 ERROR
ANALYSIS OF THE MODEL PROBLEM 195 6.3 THE GENERAL DIFFUSION EQUATION 197
6.4 BOUNDARY CONDITIONS ON A CURVED BOUNDARY 199 6.5 ERROR ANALYSIS
USING A MAXIMUM PRINCIPLE 203 6.6 ASYMPTOTIC ERROR ESTIMATES 213 6.7
VARIATIONAL FORMULATION AND THE FINITE ELEMENT METHOD 218 6.8
CONVECTION-DIFFUSION PROBLEMS 224 6.9 AN EXAMPLE V 228 BIBLIOGRAPHIC
NOTES 231 EXERCISES 232 7 ITERATIVE SOLUTION OF LINEAR ALGEBRAIC
EQUATIONS 235 7.1 BASIC ITERATIVE SCHEMES IN EXPLICIT FORM 237 7.2
MATRIX FORM OF ITERATION METHODS AND THEIR CONVERGENCE 239 7.3 FOURIER
ANALYSIS OF CONVERGENCE 244 7.4 APPLICATION TO AN EXAMPLE 248 7.5
EXTENSIONS AND RELATED ITERATIVE METHODS 250 7.6 THE MULTIGRID METHOD
252 7.7 THE CONJUGATE GRADIENT METHOD 258 7.8 A NUMERICAL EXAMPLE:
COMPARISONS 261 BIBLIOGRAPHIC NOTES 263 EXERCISES 263 REFERENCES 267
INDEX 273 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T13:15:57Z |
| indexdate | 2024-07-09T20:26:19Z |
| institution | BVB |
| isbn | 0521607930 9780521607933 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014161203 |
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| physical | XIII, 278 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Morton, Keith W. 1930- Verfasser (DE-588)172264766 aut Numerical solution of partial differential equations K.W. Morton and David Mayers 2. ed. New York Cambridge University Press 2005 XIII, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Mayers, David F. Sonstige oth HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014161203&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 | Morton, Keith W. 1930- Numerical solution of partial differential equations Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4128130-5 (DE-588)4042805-9 |
| title | Numerical solution of partial differential equations |
| title_auth | Numerical solution of partial differential equations |
| title_exact_search | Numerical solution of partial differential equations |
| title_exact_search_txtP | Numerical solution of partial differential equations |
| title_full | Numerical solution of partial differential equations K.W. Morton and David Mayers |
| title_fullStr | Numerical solution of partial differential equations K.W. Morton and David Mayers |
| title_full_unstemmed | Numerical solution of partial differential equations K.W. Morton and David Mayers |
| title_short | Numerical solution of partial differential equations |
| title_sort | numerical solution of partial differential equations |
| topic | Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Partielle Differentialgleichung Numerisches Verfahren Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014161203&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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