On nonlinear methods for stiff and singular first order initial value problems

Abstract

This paper considers development of nonlinear method by interpolation and collocation of inverse polynomial approximate solution to give systems of equations, solving for the unknown parameters and substituting the results into the approximate solution gives a continuous method. We evaluated the continuous method at different grid points to give discrete methods which are implemented without developing separate predictors. The method is convergent and A-stable, numerical examples show that the method is good for stiff and singular problems.