A modified taylor series method for solving initial-value problems in ordinary differential equations

Abstract

A one-step algorithm for solving ordinary differential equations with initial conditions is developed. Given the p first derivatives of y(x), the unknown function determined by the differential equation, this algorithm provides a method with a local discretization error of order 2p+1 instead of p+1 as is to be expected if we use the standard Taylor method with p derivatives. Several examples are given which illustrate the behaviour of the proposed algorithm and are also used to compare the efficiency of this algorithm, in terms of the computer time needed to attain a given final error tolerance, with other commonly applied techniques, such as Runge-Kutta or Adams-Moulton. The range of applicability of the method is also considered.

Keywords:

• Ordinary differential equations
• Initial-value problem
• Taylor series method

C. R. Categories:

• G.1.7