Contributions to the mathematics of the nonstandard finite difference method and applications
Copyright policy )Contributions to the mathematics of the nonstandard finite difference method and applications
AbstractWe formalize the transfer of essential properties of the solution of a differential equation to the solution of a discrete scheme as qualitative stability with respect to the properties. This permits us to motivate some rules (viz. on the order of the difference equation, on the renormalization of the denominator of the discrete derivative, and on nonlocal approximation of nonlinear terms) used in the design of nonstandard finite difference schemes. Extensions of some models are considered, and numerical examples confirming the efficiency of the nonstandard approach are provided. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 518–543, 2001
- University of Pretoria South Africa
- Vista University South Africa
Finite difference and finite volume methods for ordinary differential equations, non-standard difference methods, elementary stability, Nonlinear ordinary differential equations and systems, property preserving, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
Finite difference and finite volume methods for ordinary differential equations, non-standard difference methods, elementary stability, Nonlinear ordinary differential equations and systems, property preserving, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
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