Comparative Study of a Class of One-Step Methods for the Numerical Solution of Some Initial Value Problems in Ordinary Differential Equations

We emphasized explicitly on the derivation and implementation of a new one-step numerical method for the solution of initial value problems in ordinary differential equations. In this paper, we aimed at comparing the newly developed method with other existing methods such as Euler’s method, Trapezoidal rule and Simpson’s rule. Using these methods to solve some initial value problems of first order ordinary differential equations, we discovered that the results compared favorably, which led to the conclusion that the newly derived one-step numerical method is approximately correct and can be used for any related first order ordinary differential equations.