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This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.
Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the "principle of dynamic consistency" and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.
Sample Chapter(s)
Preface
0. A second Edition ... Why?
Contents:
- A Second Edition ... Why?
- Introduction
- Numerical Instabilities
- Nonstandard Finite Difference Schemes
- First-Order ODE's
- Second-Order, Nonlinear Oscillator Equations
- Two First-Order, Coupled Ordinary Differential Equations
- Partial Differential Equations
- Schrödinger Differential Equations
- The NSFD Methodology
- Some Exact Finite Difference Schemes
- Applications and Related Topics
- Appendices:
- Difference Equations
- Linear Stability Analysis
- Discrete WKB Method
Readership: This book is critical reading for anyone interested in the numerical integration of differential equations by use of finite differences. It is for both advanced undergraduate and graduate students, as well as researchers and practitioners in the field of numercial analysis. Selected sections of this book could provide supplementary materials for courses, both elementary and advanced, in difference and/or differential equations. Such courses exist in all of the natural and engineering sciences.
