Abstract
In this paper, a new one-step scheme was developed for the solution of initial value problems of first order in ordinary differential equations. In its development a combination of interpolating function and Taylor series were used. The method was used for the solution of initial value problems emanated from real life situations. The numerical results showed that the new scheme is consistent, robust and efficient.
Highlights
In the past years, a large number of methods suitable for solving ordinary differential equations have been proposed
The approach for the solution of initial value problems in ordinary differential equations based on numerical approximations were developed before the existence of programmable computers
Development of numerical integrator for the solution of initial value problems in ordinary differential equations has attracted the attention of many researchers in recent years
Summary
A large number of methods suitable for solving ordinary differential equations have been proposed. A major impetus to developing numerical procedures was the invention of calculus by Newton and Leibnitz, as this led to accurate mathematical models for physical reality, such as Sciences, Engineering, Medicine and Business These mathematical models cannot be usually solved explicitly and numerical method to obtain approximate solutions is needed. The approach for the solution of initial value problems in ordinary differential equations based on numerical approximations were developed before the existence of programmable computers. Development of numerical integrator for the solution of initial value problems in ordinary differential equations has attracted the attention of many researchers in recent years. If the solution to (1) posseses a singularity point, a numerical integration formulae will be more effective In another development, [10] recently discussed one-step method of Euler-Maruyama type for the solution of stochastic differential equations using varying step sizes.
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