1. A novel high order compact ADI scheme for two dimensional fractional integro-differential equations
- Author
-
Yuxiang Liang, Yan Mo, and Zhibo Wang
- Subjects
Numerical Analysis ,Differential equation ,Applied Mathematics ,Numerical analysis ,010103 numerical & computational mathematics ,01 natural sciences ,Fractional calculus ,010101 applied mathematics ,Computational Mathematics ,Alternating direction implicit method ,Norm (mathematics) ,Convergence (routing) ,Applied mathematics ,Order (group theory) ,Integration by parts ,0101 mathematics ,Mathematics - 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 H 1 norm are proved, with the accuracy order O ( τ 2 + h 1 4 + h 2 4 ) , where τ , h 1 and h 2 are temporal and spatial step sizes, respectively. Finally, numerical results are presented to support the theoretical analysis.
- Published
- 2021