A New Numerical Integrator for the Solution of Initial Value Problems in Ordinary Differential Equations. The Pacific

Abstract

ABSTRACT This research paper presents the development, analysis, and implementation of a new numerical integrator capable of solving first order initial value problems in ordinary differential equations. The algorithm developed is based on a local representation of the theoretical solution ( ) y x to the initial value problem by a nonlinear interpolating function (comprising of the combination of polynomial, exponential and cyclometric functions). The integrator is further applied on sampled problems to generate numerical results. From the results obtained, the new numerical integrator can be said to be computationally reliable and ingenious