A Numerical Technique for Direct Solution of Special Fourth Order Ordinary Differential Equation Via Hybrid Linear Multistep Method

Year 2021, Volume: 18 Issue: 1, 47 - 60, 01.05.2021

Tiamiyu Abd'gafar , Falade Kazeem Iyanda , Quadri Rauf , Sıkırulaı Akande

https://izlik.org/JA57NX85GC

Abstract

We propose and present a self-starting numerical approximation with a higher order
of accuracy for direct solution of a special fourth-order ordinary differential equation
(ODE) using a Hybrid Linear Multistep Method (HLMM). The technique utilizes the
collocation and interpolation approach with six-step numbers and two off-step points
using power series as the basis function. Error constants and basic properties proved
the convergence of the method. Numerical experiments involving both linear, nonlinear, and linear systems of fourth-order initial value problems appearing in modeling
of physical phenomenon from various areas of applied sciences were used to demonstrate the effectiveness and efficiency of the proposed method. The results revealed that
the proposed method is an excellent choice for approximating general fourth-order ODE
and shows the impact of choices of step sizes in the numerical solution of the problem
considered. In addition, the proposed HLMM outperformed existing methods in the
literature in terms of accuracy

Keywords

HLMM , Numerical approximation , Fourth-order ordinary differential equation , Self-starting

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