Numerical solution of nonlinear mixed Volterra-Fredholm integro-differential equations by two-dimensional block-pulse functions

Abstract This paper proposed an effective numerical method to obtain the solution of nonlinear two-dimensional mixed Volterra-Fredholm integro-differential equations. For this purpose, the two-dimensional block-pulse functions (2D-BPFs) operational matrix of integration and differentiation has been presented. The 2D-BPFs method converts nonlinear two-dimensional mixed Volterra-Fredholm integro-differential equations to an algebraic system of equations which is computable as well. Error analysis and some numerical examples are presented to illustrate the effectiveness and accuracy of the method.