Nonstandard finite difference schemes for differential equations

Abstract

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with standard methods.

Keywords

• Finite difference
• Nonstandard
• Singular
• Predator-prey model
• Heat equation