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A novel high order compact ADI scheme for two dimensional fractional integro-differential equations.
- Source :
-
Applied Numerical Mathematics . Sep2021, Vol. 167, p257-272. 16p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *INTEGRO-differential equations
*INTEGRALS
Subjects
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 167
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 150639941
- Full Text :
- https://doi.org/10.1016/j.apnum.2021.05.008