Application of Bernstein Polynomials for Solving Linear Volterra Integro-Differential Equations with Convolution Kernels

Abstract

This paper deals with a new application of Bernstein polynomials to find approximate solution of linear Volterra Integro-differential
equation of a special kind. For this purpose, we first need to convert multiple integral into single integral. Since we have taken kernel of convolution type so we will use convolution product. By using properties of Bernstein polynomials integral equation is reduced into an algebraic equation. The set of algebraic equation is then solved and approximate solution is obtained. Some numerical solutions are also presented to confirm the reliability and applicability of the proposed method.