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

In this article, the current work suggests an efficient numerical approximation based on an operational matrix of Bernstein Polynomials to obtain numerical solution of high-order of integro-differential equations. At first, we present the integral and differential operator matrix of Bernstein Polynomials, and then apply this operator to the governing equation to transform it into an algebraic equations. Solving this system yields an approximate solution for the equation under study. Also, the convergence and error analysis for this method are study. To demonstrate the effectiveness of this scheme, we provide several numerical examples and compare the results with the exact solution and one of the other well-known method such as collocation Bernoulli method..