A hybrid-based numerical method for a class of systems of mixed Volterra–Fredholm integral equations

This study introduces a hybrid procedure based on a block-by-block scheme (created by the Gauss–Lobatto integration formula) and a set of the hybrid functions (defined by the Legendre polynomials and block-pulse functions) to solve a class of systems of mixed Volterra–Fredholm integral equations. More precisely, the proposed scheme combines the Gauss–Lobatto quadrature rule for the temporal variable and the hybrid functions for the spacial direction. In the established procedure, several values of the problem solution are elicited simultaneously, without employing any starting value for beginning. The convergence, along with the analysis of error for the method are proved. Some numerical examples are solved to show the efficiency and accuracy of the proposed strategy.