On rotated grid point iterative method for solving 2D fractional reaction-subdiffusion equation with Caputo-Fabrizio operator. (English) Zbl 1481.65116
Summary: In this paper, the Crank-Nicolson (CN) and rotated four-point Fractional Explicit Decoupled Group (FEDG) methods are introduced to solve the two-dimensional reaction-subdiffusion equation with Caputo-Fabrizio operator. The FEDG method is derived by \(45^{\circ}\) rotation of CN method around the \(x\) and \(y\) axes. The restarted GMRES with left preconditioner L, based on incomplete LU factorization is used to solve the discretized system obtained by our proposed methods. The FEDG method shows more superior capability in the term of CPU timings and the number of iteration compared to CN method on the standard grid but with same order of accuracy. The stability and convergence analysis in the approximate schemes are investigated. Some numerical experiments performed to show the efficiency of the presented methods in terms of accuracy and CPU time.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65F08 | Preconditioners for iterative methods |
| 65F10 | Iterative numerical methods for linear systems |
| 65D30 | Numerical integration |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
Keywords:
reaction-subdiffusion equation; Caputo-Fabrizio operator; Crank-Nicolson method; explicit decoupled group method; stability; convergenceReferences:
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