Numerical Solution of Fourth Order Linear Ordinary Differential Equations by Cubic Spline Collocation Tau Method

Abstract

Problem Statement: Many boundary value problems that arise in real life situations defy analytical solution; hence numerical techniques are desirable to find the solution of such equations. New numerical methods which are comparatively better than the existing ones in terms of efficiency, accuracy, stability, convergence and computational cost are always needed. Approach: In this study, we developed and applied three methods-standard cubic spline collocation, perturbed cubic spline collocation and perturbed cubic spline collocation tau method with exponential fitting, for solving fourth order boundary value problems. A mathematical software MATLAB was used to solve the systems of equations obtained in the illustrative examples. Results: The results obtained, from numerical examples, show that the methods are efficient and accurate with perturbed cubic spline collocation tau method with exponential fitting been the most efficient and accurate method with little computational effort involved. Conclusion: These methods are preferable to some existing methods because of their simplicity, accuracy and less computational cost involved.