Difference Approximation for 2D Time-Fractional Integro-Differential Equation with Given Initial and Boundary Conditions

Abstract

In this investigation, a new algorithm based on the compact difference method is proposed. The purpose of this investigation is to solve the 2D time-fractional integro-differential equation. The Riemann–Liouville derivative was utilized to define the time-fractional derivative. Meanwhile, the weighted and shifted Grünwald difference operator and product trapezoidal formula were utilized to construct a high-order numerical scheme. Also, we analyzed the stability and convergence. The convergence order was O(τ2+hx4+hy4), where τ is the time step size, hx and hy are the spatial step sizes. Furthermore, several examples were provided to verify the correctness of our theoretical reasoning.

Keywords

• integro-differential equation
• Riemann–Liouville derivative
• compact finite difference method
• stability
• convergence