应用与计算数学杂志

Approximate Solution to First-order Integro-differential Equations Using Polynomial Collocation Approach

Abstract

Ganiyu Ajileye and F.A. Aminu

In this study, power series and shifted Chebyshev polynomials are used as basis function for solving first order volterra integro-differential equations using standard collocation method. An assumed approximate solution in terms of the constructed polynomial was substituted into the class of integro-differential equation considered. The resulted equation was collocated at appropriate points within the interval of consideration [0,1] to obtain a system of algebraic linear equations. Solving the system of equations, by inverse multiplication, the unknown coefficients involved in the equations are obtained. The required approximate results are obtained when the values of the constant coefficients are substituted back into the assumed approximate solution. Numerical example are presented to confirm the accuracy and efficiency of the method.