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Li, Changpin; Yi, Qian

Finite difference method for two-dimensional nonlinear time-fractional subdiffusion equation. (English) Zbl 1428.65010

Fract. Calc. Appl. Anal. 21, No. 4, 1046-1072 (2018).
Summary: In this article, we propose an implicit-explicit scheme combining with the fast solver in space to solve two-dimensional nonlinear time-fractional subdiffusion equation. The applications of implicit-explicit scheme and fast solver will smartly enhance the computational efficiency. Due to the non-smoothness (or low regularities) of solutions to fractional differential equations, correction terms are introduced in the proposed scheme to improve the accuracy of error. The stability and convergence of the present scheme are also investigated. Numerical examples are carried out to demonstrate the efficiency and applicability of the derived scheme for both linear and nonlinear fractional subdiffusion equations with non-smooth solutions.

Cited in 15 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
15A18 Eigenvalues, singular values, and eigenvectors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

time-fractional subdiffusion equation; implicit-explicit scheme; fast solver; correction terms

Software:

ma2dfc
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References:

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