Nonstandard finite difference models of differential equations:
This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary typ...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific Pub. Co.
c1994
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| Subjects: | |
| Online Access: | FHN01 Volltext |
| Summary: | This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of "exact" and "best" finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation |
| Physical Description: | xi, 249 p. ill |
| ISBN: | 9789814440882 |
Staff View
MARC
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| 520 | |a This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of "exact" and "best" finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation | ||
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044639232 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:55Z |
| institution | BVB |
| isbn | 9789814440882 |
| language | English |
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| physical | xi, 249 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| spelling | Mickens, Ronald E. 1943- Verfasser aut Nonstandard finite difference models of differential equations Ronald E. Mickens Singapore World Scientific Pub. Co. c1994 xi, 249 p. ill txt rdacontent c rdamedia cr rdacarrier This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of "exact" and "best" finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation Finite differences Differential equations / Numerical solutions Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Finite-Differenzen-Methode (DE-588)4194626-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Finite-Differenzen-Methode (DE-588)4194626-1 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9789810214586 Erscheint auch als Druck-Ausgabe 9810214588 http://www.worldscientific.com/worldscibooks/10.1142/2081#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mickens, Ronald E. 1943- Nonstandard finite difference models of differential equations Finite differences Differential equations / Numerical solutions Differentialgleichung (DE-588)4012249-9 gnd Finite-Differenzen-Methode (DE-588)4194626-1 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4194626-1 |
| 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 | Finite differences Differential equations / Numerical solutions Differentialgleichung (DE-588)4012249-9 gnd Finite-Differenzen-Methode (DE-588)4194626-1 gnd |
| topic_facet | Finite differences Differential equations / Numerical solutions Differentialgleichung Finite-Differenzen-Methode |
| url | http://www.worldscientific.com/worldscibooks/10.1142/2081#t=toc |
| work_keys_str_mv | AT mickensronalde nonstandardfinitedifferencemodelsofdifferentialequations |