The method of discretization in time and partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Czech |
| Published: |
Dordrecht u.a.
Reidel
1982
|
| Series: | Mathematics and its applications / East European series
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 451 S. |
| ISBN: | 9027713421 |
Staff View
MARC
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| 245 | 1 | 0 | |a The method of discretization in time and partial differential equations |
| 264 | 1 | |a Dordrecht u.a. |b Reidel |c 1982 | |
| 300 | |a XVIII, 451 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications / East European series |v 4 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Editor s Preface IX
Preface XI
Notation Frequently Used XV
Chapter 1. Introduction 1
Chapter 2. A Brief Survey of Variational Methods 8
Part I. EXAMPLES 66
Chapter 3. Algorithm of the Method. Error Estimates 68
a) Algorithm of the method 68
b) Error estimates 81
Chapter 4. Linear Parabolic Problems 85
a) Illustrative examples 86
a) Homogeneous initial conditions 86
P) Nonhomogeneous initial conditions 94
b) A nontrivial example 107
c) An equation with time dependent coefficients 118
Chapter 5. A Nonlinear Problem 127
Chapter 6. An Integrodifferential Parabolic Problem 137
Chapter 7. A Problem with an Integral Condition 147
Chapter 8. Hyperbolic Problems 157
Chapter 9. An Application to Rheology 170
Part II. THEORETICAL ASPECTS OF THE METHOD OF DISCRE¬
TIZATION IN TIME
Chapter 10. Introduction to Part II 185
Chapter 11. The Equation cujct + Au =/. Existence and Conver¬
gence Theorem 187
Chapter 12. Regularity Questions. Error Estimates 219
a) Smoother solutions 219
VII
VIII Contents
a) Regularity with respect to t 219
P) Regularity with respect to x 231
b) Error estimates 237
Chapter 13. Nonhomogeneous Initial and Boundary Conditions 247
a) Nonhomogeneous initial conditions. The very weak
solution 249
b) Regularity of the very weak solution. Problem of
error estimates 257
c) Nonhomogeneous boundary conditions 268
d) The problem (13.1) —(13.4) 274
Chapter 14. Approximate Solution of Elliptic Problems Generated by
the Method of Discretization in Time 277
Chapter 15. Problem with Time Variable Coefficients 283
Chapter 16. Nonlinear Parabolic Problems 305
a) Basic concepts. The Gateaux differential 307
b) An existence and convergence theorem 314
c) Numerical solution of elliptic problems generated by
the method of discretization in time 327
Chapter 17. Integrodifferential Parabolic Problems 335
Chapter 18. A Problem with an Integral Condition 358
Chapter 19. Hyperbolic Problems. Homogeneous Initial Conditions.
Existence and Convergence Theorem. Error Estimate 382
a) Existence and convergence 382
b) Error estimate 399
Chapter 20. Hyperbolic Problems. Nonhomogeneous Initial Conditions 410
Chapter 21. Concluding Remarks 430
a) Some other properties of the obtained solutions 430
a) Lipschitz continuity 430
P) u e Ljj, V), u e Ljl, L2{G)) 431
y) «„ u in C(I, V) 431
b) Replacing F ellipticity by F coercivity 433
c) Concerning the function / 434
d) Time dependent stable boundary conditions 437
e) Nonhomogeneous unstable boundary conditions 440
References • 446
Subject index 449
|
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/5 |
| dewey-search | 515.3/5 |
| dewey-sort | 3515.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000157633 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:09:33Z |
| institution | BVB |
| isbn | 9027713421 |
| language | English Czech |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000088943 |
| oclc_num | 239756406 |
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| owner_facet | DE-12 DE-739 DE-19 DE-BY-UBM DE-29T DE-703 DE-706 DE-11 DE-188 DE-634 |
| physical | XVIII, 451 S. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Reidel |
| record_format | marc |
| series2 | Mathematics and its applications / East European series |
| spelling | Rektorys, Karel Verfasser aut The method of discretization in time and partial differential equations Dordrecht u.a. Reidel 1982 XVIII, 451 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / East European series 4 Boundary value problems Numerical solutions Differential equations, Parabolic Numerical solutions Evolution equations Numerical solutions Diskretisierung (DE-588)4012469-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Diskretisierung (DE-588)4012469-1 s DE-604 Evolutionsgleichung (DE-588)4129061-6 s Numerisches Verfahren (DE-588)4128130-5 s Parabolische Differentialgleichung (DE-588)4173245-5 s Randwertproblem (DE-588)4048395-2 s East European series Mathematics and its applications 4 (DE-604)BV000006709 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000088943&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rektorys, Karel The method of discretization in time and partial differential equations Boundary value problems Numerical solutions Differential equations, Parabolic Numerical solutions Evolution equations Numerical solutions Diskretisierung (DE-588)4012469-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Randwertproblem (DE-588)4048395-2 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4012469-1 (DE-588)4128130-5 (DE-588)4129061-6 (DE-588)4048395-2 (DE-588)4173245-5 |
| title | The method of discretization in time and partial differential equations |
| title_auth | The method of discretization in time and partial differential equations |
| title_exact_search | The method of discretization in time and partial differential equations |
| title_full | The method of discretization in time and partial differential equations |
| title_fullStr | The method of discretization in time and partial differential equations |
| title_full_unstemmed | The method of discretization in time and partial differential equations |
| title_short | The method of discretization in time and partial differential equations |
| title_sort | the method of discretization in time and partial differential equations |
| topic | Boundary value problems Numerical solutions Differential equations, Parabolic Numerical solutions Evolution equations Numerical solutions Diskretisierung (DE-588)4012469-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Randwertproblem (DE-588)4048395-2 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Boundary value problems Numerical solutions Differential equations, Parabolic Numerical solutions Evolution equations Numerical solutions Diskretisierung Numerisches Verfahren Evolutionsgleichung Randwertproblem Parabolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000088943&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006709 |
| work_keys_str_mv | AT rektoryskarel themethodofdiscretizationintimeandpartialdifferentialequations |