An efficient numerical scheme for a class of integro-differential equations with its convergence and error analysis

Abstract

In this article an efficient numerical approximation based on operational matrix of Bernstein Polynomials is used to obtain numerical solution of high order of integro-differential equations. At first, the integer and differential operator matrix of Bernstein Polynomials is shown, and this operator is applied to the governing equation to transform it into a algebraic equations. By solving this system an approximate solution for the equation under study will be determind. Also, the convergence and error analysis for this method are presented. To demonstrate the effectiveness of this scheme, several numerical examples are provided and the results are compared with the exact solution and other well-known method such as the collocation Bernoulli method