The numerical method of lines: integration of partial differential equations
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| Main Author: | |
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| Format: | Book |
| Language: | Undetermined |
| Published: |
San Diego, CA u.a.
San Diego, CA u.a.
1991
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 326 S. |
| ISBN: | 0126241309 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
1
What Is the Numerical
Method of Lines?
1 1 Why PDEs? 2
12A Typical PDE Derivation 3
1 3 Subscript Notation for PDEs 7
1 4 What Is a Solution to a PDE? 8
15A Brief Introduction to the Numerical Method of Lines 10
1 6 An Error Analysis of the NUMOL Solution 19
1 7 Dirichlet and Neumann Boundary Conditions 24
1 8 Arguments versus COMMON 31
References 43
Problems 43
2
Some Applications of
the Numerical Method of Lines
2 1 Additional COMMON 45
2 2 Inconsistent Initial and Boundary Conditions 49
vill Contents
23A Nonlinear Problem 54
24A Linear PDE In Cylindrical Coordinates:
The Parabolic Fourier Second Law 60
25A Nonlinear PDE In Spherical Coordinates 63
26A PDE Second-Order In Time: The Hyperbolic Wave Equation
2 7 Three PDEs Zero-Order in Time: The Elliptic Laplace,
Poisson, and Helmholtz Equations 75
2 8 Two Nonlinear PDEs 90
References 95
Problems 95
3
Spatial Differentiation
3 1 Polynomial Approximations 97
3 2 Second-Order Formulas for First Derivatives 98
3 3 Fourth-Order Formulas for First Derivatives 105
3 4 Fourth-Order Formulas for Second Derivatives 111
3 5 First-Order Hyperbolic PDEs 122
References 141
Problems 141
4
Initial-Value Integration
4 1 The ODE Eigenvalue Problem 147
4 2 Stability of Nonlinear ODEs 150
4 3 Stability of the Explicit Euler Method 152
4 4 Stability of the Implicit Euler Method 158
4 5 The BDF Methods 160
4 6 SDRIV2 167
4 7 LSODE, LSODES, and LSODI 171
4 8 DASSL 191
References 205
Problems 206
5
Stability of Numerical
Method of Lines Approximations
5 1 Approximations of the Advectlon Equation 209
5 2 Approximation of the Heat-Conduction Equation 213
Contents Ix
53A System of Nonlinear PDEs with Mapping and Eigenvalue
Analysis of the ODE Jacobian Matrix 215
References 244
Problems 244
6
Additional Applications:
Multidimensional PDEs
and Adaptive Grids
6 1 Classification of PDEs 246
6 2 Burgers Equation in One Dimension 250
6 3 Burgers Equation in Two Dimensions 262
6 4 Burgers Equation in Three Dimensions 273
6 5 Adaptive Grids 287
6 6 Summary and Conclusions 302
References 302
Problems 302
Appendix A
The Laplacian Operator in Various Coordinate
Systems 305
Appendix B
Spatial Differentiation Routines 307
Appendix C
Library of ODE and PDE Applications 310
Physics 310
Mathematics 311
Biochemical, Biomedical, and Environmental Systems 313
Separation Systems 314
Kinetics and Reactor Models 315
Heat Transfer 316
Fluid Flow 317
Automatic Control 318
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| id | DE-604.BV013496834 |
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| indexdate | 2024-07-09T18:46:51Z |
| institution | BVB |
| isbn | 0126241309 |
| language | Undetermined |
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| owner_facet | DE-19 DE-BY-UBM |
| physical | XIII, 326 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | San Diego, CA u.a. |
| record_format | marc |
| spelling | Schiesser, W. E. Verfasser aut The numerical method of lines integration of partial differential equations W. E. Schiesser San Diego, CA u.a. San Diego, CA u.a. 1991 XIII, 326 S. txt rdacontent n rdamedia nc rdacarrier 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 Numerische Mathematik (DE-588)4042805-9 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009212649&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 | Schiesser, W. E. The numerical method of lines integration of partial differential equations 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 | The numerical method of lines integration of partial differential equations |
| title_auth | The numerical method of lines integration of partial differential equations |
| title_exact_search | The numerical method of lines integration of partial differential equations |
| title_full | The numerical method of lines integration of partial differential equations W. E. Schiesser |
| title_fullStr | The numerical method of lines integration of partial differential equations W. E. Schiesser |
| title_full_unstemmed | The numerical method of lines integration of partial differential equations W. E. Schiesser |
| title_short | The numerical method of lines |
| title_sort | the numerical method of lines integration of partial differential equations |
| title_sub | integration of partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Partielle Differentialgleichung Numerisches Verfahren Numerische Mathematik |
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