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

摘要

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