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

摘要

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.