Numerical solutions of system of two-dimensional Volterra integral equations via operational matrices of hybrid functions

The main target of this paper is to solve a system of two-dimensional Volterra integral equations (۲-DVIEs). Operational Matrices of two-dimensional hybrid of block-pulse functions and Legendre polynomials are applied to reduce these systems of integral equations to a system of algebraic equations. The main benefit of these basic functions is their efficiency in dealing with non-sufficiently smooth functions. An error bound is provided and some examples are prepared to verify the applicability of the offered numerical technique.

Keywords:

System of two-dimensional Volterra integral equations , two-dimensional hybrid functions , oroduct Operational matrix , operational matrices of integration