Nonlinear Explicit Method for First Order Initial Value Problems

Abstract

In this research paper ,we present the development , implementation and analysis of a nonlinear explicit numerical method based on local assumption for solving first order initial value problems in ordinary differential equations. The method has at least second order accuracy and A-stable property. The property of A –stability suggests that method can be used for the solution of stiff initial value problems in ordinary differential equations. The method applied to find the numerical solution of several model problems. The computational results obtained for the model problems suggest that method is accurate, reliable and ingenious. The computational performance of the present method is comparable to the other method.