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 advance the topic.
* Applications of Mickens Discretizations to Boundary Value Problems of Bratu, Gelfand and Others (R Buckmire) * Nonstandard Finite Difference Time Domain Algorithms for Computational Electromagnetics: Applications to Current Topics in Optics and Photonics (J B Cole) * Reliable Finite Difference Schemes with Applications in Mathematical Ecology (D T Dimitrov et al.) * Application of the Nonstandard Finite Difference Method in Non-Smooth Mechanics (Y Dumont) * Finite Difference Schemes on Unbounded Domains (M Ehrhardt) * Dynamically-Consistent Nonstandard Finite Difference Methods for Epidemic Models (A Gumel & K C Patidar) * Nonstandard Finite Difference Methods and Biological Models (S R-J Jang) * Contribution to the Theory of Nonstandard Finite Difference Methods and Applications to Singular Perturbation Problems (J M-S Lubuma & K C Patidar) * Nonstandard Discretization Methods on Lotka-Volterra Differential Equations (L-I W Roeger)