A Beneficial Numerical Approach to Solve Systems of Linear Integro-Differential Equations

Abstract

The system of linear Fredholm-Volterra integro-differential equations (FVIDEs) has been solved in this paper by an improved approximation method. Generalised Bernstein polynomials and collocation points have been used to construct the theory of the method. The aim of the technique is to reduce systems of integro-differential equations into an algebraic matrix equation, which corresponds to a linear algebraic equation system, by means of Bernstein polynomials. In order to analyse the applicability of the method, some illustrative examples have also been considered. It has been shown that the proposed method is faster and more effective than the others when comparing the numerical results.