Third derivative integrator for the solution of first order initial value problems

Abstract

Most mathematical models used in physical sciences, biological sciences, medical sciences and engineering are based on Ordinary Differential Equations. Traditionally, solutions to these differential equations can be obtained using analytical methods, however, solutions to certain differential equations are very difficult except the approximate solution by the application of numerical methods. Researchers developed several numerical methods for the solution of ordinary differential equations, but the need to have more accurate numerical method has made it imperative to develop new methods that will yield better results. In this paper therefore, third derivative integrator is developed for solving ordinary differential equations using polynomial approximate solution with the resulted schemes implemented in block. Step and off-step points are considered during the derivation process. The stability properties of the new integrator are established and its accuracy tested on some numerical examples. The results obtained in this study shows that, the new integrator is more efficient for the solution of initial value problems of first order ordinary differential equations, when compared with some existing integrators. The new integrator will be useful for the solution of mathematical problems model in ordinary differential equations.