Hybrid Legendre Block-Pulse functions method for solving partial differential equations with non-local integral boundary conditions

Operational matrix method for solving partial differential equations (PDEs) with non-local boundary integral conditions is considered in this paper. this algorithm is based on the operational and almost operational matrix of integration and differentiation of the hybrid Legendre Block-Pulse functions (HLBPFs). At first, we imposed the initial and boundary conditions on the main problem to get the associated integro-PDE. Using the operational matrices and completeness of the hybrid basis, the obtained integro-PDE will be reduced to a system of algebraic equations. Convergence analysis for this scheme will be shown by preparing some theorems and lemmas. Finally, one example is given to illustrate the accuracy and capability of the proposed algorithm with compared to some other well-known methods.