A New Self-Adjusting Numerical Integrator for the Numerical Solutions of Ordinary Differential Equations

Abstract

In this work, we consider a class of formulae for the numerical solution of IVP, in ordinary differential equations with point of singularity, in which the underlying interpolant is a rational function. This is in contrast with the classical formulae which are in general based on polynomial approximation. The proof of convergence and consistency for the scheme are also given. There are two parameters that control the position and the nature of singularity. The values of these parameters are automatically chosen and revised, during the computation.