Sumudu-Bernstein solution of differential, integral and integro-differential equations

Abstract

A numerical method based on the inverse Sumudu transform and the Bernstein polynomials operational matrix of integration is developed. The derived method is implemented in solving linear differential, integral and integro-differential equations. Also, a procedure for overcoming nonlinearity is developed and implemented to solve nonlinear Volterra integral equations. The approximate results are compared with the exact solutions and an existing method. Error estimation shows that the proposed method has elevated level of accuracy for just a few terms of the polynomial.