Applications of nonstandard finite difference schemes:
The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous w...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
[2000]
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| Schlagworte: | |
| Online-Zugang: | FHN01 UBM01 Volltext |
| Zusammenfassung: | The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection–diffusion–reaction equations that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. Chapter 5 discusses exactness, stability properties, and the symplecticity of various schemes including the conditions for which Runge–Kutta methods are exact. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used. This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena |
| Beschreibung: | 1 Online-Ressource (xii, 250 S.) Illustrationen |
| ISBN: | 9789812813251 |
| DOI: | 10.1142/4272 |
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| 520 | |a The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection–diffusion–reaction equations that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. Chapter 5 discusses exactness, stability properties, and the symplecticity of various schemes including the conditions for which Runge–Kutta methods are exact. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used. This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1142/4272 |
| format | Electronic eBook |
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| isbn | 9789812813251 |
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| spelling | Applications of nonstandard finite difference schemes editor Ronald E. Mickens Singapore World Scientific Pub. Co. [2000] 1 Online-Ressource (xii, 250 S.) Illustrationen txt rdacontent c rdamedia cr rdacarrier The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection–diffusion–reaction equations that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. Chapter 5 discusses exactness, stability properties, and the symplecticity of various schemes including the conditions for which Runge–Kutta methods are exact. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used. This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena Differential equations, Partial / Numerical solutions Finite differences 1\p (DE-588)1071861417 Konferenzschrift gnd-content Mickens, Ronald Elbert 1943- (DE-588)172258324 edt Erscheint auch als Druck-Ausgabe 9789810241339 Erscheint auch als Druck-Ausgabe 981024133X https://doi.org/10.1142/4272 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Applications of nonstandard finite difference schemes Differential equations, Partial / Numerical solutions Finite differences |
| subject_GND | (DE-588)1071861417 |
| title | Applications of nonstandard finite difference schemes |
| title_auth | Applications of nonstandard finite difference schemes |
| title_exact_search | Applications of nonstandard finite difference schemes |
| title_full | Applications of nonstandard finite difference schemes editor Ronald E. Mickens |
| title_fullStr | Applications of nonstandard finite difference schemes editor Ronald E. Mickens |
| title_full_unstemmed | Applications of nonstandard finite difference schemes editor Ronald E. Mickens |
| title_short | Applications of nonstandard finite difference schemes |
| title_sort | applications of nonstandard finite difference schemes |
| topic | Differential equations, Partial / Numerical solutions Finite differences |
| topic_facet | Differential equations, Partial / Numerical solutions Finite differences Konferenzschrift |
| url | https://doi.org/10.1142/4272 |
| work_keys_str_mv | AT mickensronaldelbert applicationsofnonstandardfinitedifferenceschemes |