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This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and engineering sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to adv

Differential equations, Partial --- Differential equations --- Finite differences. --- Differences, Finite --- Finite difference method --- Numerical analysis --- 517.91 Differential equations --- Numerical solutions.

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Mathematical analysis

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Differential equations, Nonlinear --- Approximation theory --- Nonlinear oscillations --- Equations différentielles non linéaires --- Théorie de l'approximation --- Oscillations non linéaires --- Numerical solutions --- Solutions numériques

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Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations; nonlinear equations that may be reduced to linear equations; and partial difference equations.

Difference equations. --- Équations aux différences.