A Non-standard discrete model for the solution of first order Ordinary Differential Equations using minimally characterized interpolating function

Abstract

We present a new set of one step finite difference schemes for the numerical solution of  First order differential equations using a combination of an interpolation function and a modification of the resulting schemes by replacing step size  with a suitable function of   as required by the second non-standard modeling rule. The resulting schemes have been applied to some initial value problems and the schemes have been found to possess  desirable qualitative properties.

KEYWORDS

Nonstandard methods, Hybrid, Interpolation functions, Non-standard modeling rules, Standard Finite difference methods