A novel approach to solving system of integral partial differential equations based on hybrid modified block‐pulse functions

Abstract

In nonlinear this paper, we present a new approach to solve system of two‐dimensionalFredholm–Volterra integral partial differential equations. This approach is based on a new hybrid of two‐dimensional Bernoulli polynomials and modified block‐pulse functions. Different from the traditional methods, in this new approach, the operational matrices are considered. Furthermore, by solving this matrix equation and using the collocation method, approximate solutions for the problem are obtained. Finally, error analysis and three practical examples are provided accuracy and efficiency illustrate our approach.