Numerical inversion of Sumudu transform by orthonormal bernstein polynomials

Abstract

An approximate method based on operational matrix of integration of the orthonormal Bernstein polynomials is developed for the inversion of Sumudu transform. The procedure is based on replacing the unknown function through a truncated series of Bernstein polynomials basis while the coefficients of the expansion are obtained using the operational matrix of integration. Error estimation is performed, convergence analysis is carried out using the residual function and the proof shows that the residual function is Cauchy convergent. A test of the proposed method is performed on some Sumudu transforms and the results of their inverse functions as well as their error estimates are obtained. A comparison of the results and the errors with the exact solution and the existing method respectively shows that the proposed method has elevated level of accuracy for just a few terms of the polynomial and it is better than the existing approach.