A novel high order compact ADI scheme for two dimensional fractional integro-differential equations

Abstract

In this paper, we study the numerical method for two dimensional fractional integro-differential equations, where the order of time fractional derivative α∈(1,2) and integral order γ∈(0,1). To overcome the difficulty caused by the two fractional terms, we transform the original equation using the method of integration by parts. A novel high order compact alternating direction implicit (ADI) difference scheme is then proposed to solve the equivalent model. By some skills and detailed analysis, the unconditional stability and convergence in H1 norm are proved, with the accuracy order O(τ2+h14+h24), where τ,h1 and h2 are temporal and spatial step sizes, respectively. Finally, numerical results are presented to support the theoretical analysis.