Numerical Solution of Fourth order Integro-Differential Equations by Least Square Approximation Method using Chebyshev Polynomials as Basis Function

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Date

2023-03

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JOURNAL OF SCIENCE TECHNOLOGY AND EDUCATION

Abstract

In this paper, Least square approximation method is used as numerical solution of fourth order integro-differential equations using Chebyshev polynomials of the first kind as basis function. The method assumed an approximate solution using Chebyshev polynomial functions which are then substituted into the problem considered. Then the like terms of the unknown coefficients are collected and simplified. The resulting equation is minimized using the least square approximation, thus resulted into linear algebraic systems of equations which are then solved by Gaussian Elimination method, to obtain the unknown constants substituted back into the assumed approximate solution to get the required approximate solution. Numerical solutions are given to illustrate the accuracy of the methods discussed in the work. Also, absolute errors of the problem are presented in tabular forms.

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Gaussian Elimination method, Least square method, Integro-Differential equation

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