Numerical scheme for solving system of fractional partial differential equations with Volterra-type integral term through two-dimensional block-pulse functions

摘要

In the current study, an approximate scheme is established for solving the fractional partial differential equations (FPDEs) with Volterra integral terms via two-dimensional block-pulse functions (2D-BPFs). According to the definitions and properties of 2D-BPFs, the original problem is transformed into a system of linear algebra equations. By dispersing the unknown variables for these algebraic equations, the numerical solutions can be obtained. Besides, the proof of the convergence of this system is given. Finally, several numerical experiments are presented to test the feasibility and effectiveness of the proposed method.