Nonstandard finite difference models of differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 249 S. graph. Darst. |
| ISBN: | 9810214588 |
Internformat
MARC
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| 100 | 1 | |a Mickens, Ronald E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonstandard finite difference models of differential equations |c Ronald E. Mickens |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1994 | |
| 300 | |a XI, 249 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Equations aux différences |2 ram | |
| 650 | 7 | |a Equations différentielles - Solutions numériques |2 ram | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Finite differences | |
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Datensatz im Suchindex
| _version_ | 1804124056235016192 |
|---|---|
| adam_text | ix
Table of Contents
1. Introduction 1
1.1 Numerical Integration 1
1.2 Standard Finite Difference Modeling Rules 2
1.3 Examples 4
1.4 Critique 13
References 14
2. Numerical Instabilities 17
2.1 Introduction 17
2.2 Decay Equation 18
2.3 Harmonic Oscillator 29
2.4 Logistic Differential Equation 35
2.5 Unidirectional Wave Equation 51
2.6 Burgers Equation 58
2.7 Summary 60
References 65
3. Nonstandard Finite Difference Schemes 68
3.1 Introduction 68
3.2 Exact Finite Difference Schemes 70
3.3 Examples of Exact Schemes 72
3.4 Nonstandard Modeling Rules 81
3.5 Best Finite Difference Schemes 85
References 90
4. First Order ODE s 93
4.1 Introduction 93
4.2 A New Finite Difference Scheme 94
4.3 Examples 98
4.4 Nonstandard Schemes 106
4.5 Discussion 115
References 119
X
5. Second Order, Nonlinear Oscillator Equations 120
5.1 Introduction 120
5.2 Mathematical Preliminaries 122
5.3 Conservative Oscillators 124
5.4 Limit Cycle Oscillators 132
5.5 General Oscillator Equations 137
5.6 Response of a Linear System 138
References 141
6. Two First Order, Coupled Ordinary Differential Equations 144
6.1 Introduction 144
6.2 Background 146
6.3 Exact Scheme for Linear Ordinary Differential Equations 147
6.4 Nonlinear Equations 150
6.5 Examples 151
6.6 Summary 162
References 163
7. Partial Differential Equations 165
7.1 Introduction 165
7.2 Wave Equations 166
7.3 Diffusion Equations 173
7.4 Burgers Type Equations 182
7.5 Discussion 188
References 189
8. Schrodinger Differential Equations 193
8.1 Introduction 193
8.2 Schrodinger Ordinary Differential Equations 194
8.3 Schrodinger Partial Differential Equations 198
References 213
9. Summary and Discussion 217
9.1 Resume 217
9.2 Nonstandard Modeling Rules Revisited 219
9.3 Two Examples 223
9.4 Future Directions 229
References 230
i xi
Appendix A: Difference Equations 232
Appendix B: Linear Stability Analysis 236
Appendix C: Discrete WKB Method 239
Bibliography 241
Index 247
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:39:36Z |
| institution | BVB |
| isbn | 9810214588 |
| language | English |
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| physical | XI, 249 S. graph. Darst. |
| publishDate | 1994 |
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| publishDateSort | 1994 |
| publisher | World Scientific |
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| spelling | Mickens, Ronald E. Verfasser aut Nonstandard finite difference models of differential equations Ronald E. Mickens Singapore u.a. World Scientific 1994 XI, 249 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Equations aux différences ram Equations différentielles - Solutions numériques ram Differential equations Numerical solutions Finite differences Finite-Differenzen-Methode (DE-588)4194626-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Finite-Differenzen-Methode (DE-588)4194626-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006421668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mickens, Ronald E. Nonstandard finite difference models of differential equations Equations aux différences ram Equations différentielles - Solutions numériques ram Differential equations Numerical solutions Finite differences Finite-Differenzen-Methode (DE-588)4194626-1 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4194626-1 (DE-588)4012249-9 |
| title | Nonstandard finite difference models of differential equations |
| title_auth | Nonstandard finite difference models of differential equations |
| title_exact_search | Nonstandard finite difference models of differential equations |
| title_full | Nonstandard finite difference models of differential equations Ronald E. Mickens |
| title_fullStr | Nonstandard finite difference models of differential equations Ronald E. Mickens |
| title_full_unstemmed | Nonstandard finite difference models of differential equations Ronald E. Mickens |
| title_short | Nonstandard finite difference models of differential equations |
| title_sort | nonstandard finite difference models of differential equations |
| topic | Equations aux différences ram Equations différentielles - Solutions numériques ram Differential equations Numerical solutions Finite differences Finite-Differenzen-Methode (DE-588)4194626-1 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Equations aux différences Equations différentielles - Solutions numériques Differential equations Numerical solutions Finite differences Finite-Differenzen-Methode Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006421668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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