Comparison of Adams-Bashforth-Moulton Method and Milne-Simpson Method on Second Order Ordinary Differential Equation

Adekoya Odunayo M.^1, and Z.O. Ogunwobi¹

¹Department of Mathematics Olabisi Onabanjo University, Ogun State, Nigeria

Cite this paper:
Adekoya Odunayo M. and Z.O. Ogunwobi. Comparison of Adams-Bashforth-Moulton Method and Milne-Simpson Method on Second Order Ordinary Differential Equation. Turkish Journal of Analysis and Number Theory. 2021; 9(1):1-8. doi: 10.12691/tjant-9-1-1

Abstract

This work considers the use of Adam Bashforth-Moulton method and Milne Simpson method to solve second order ordinary differential equation with initial value problem and to compare solution with the exact solution, to solve that we first convert the equation to two set of first order differential equation by order reduction method, then we use a single step method for approximation of initially orders which are required to start the linear multistep method. The result show that the numerical solutions are in good agreement with the exact solution. The result show that Adam Bashforth-Moulton method is better than Milne Simpson method in solving differential equation of second order.

Keywords:
second order differential equation Adam Bashforth Moulton Method Milne Simpson method convergence

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