A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model. (English) Zbl 1452.65175
Summary: In this paper, we present a time two-grid algorithm based on the finite difference (FD) method for the two-dimensional nonlinear time-fractional mobile/immobile transport model. We establish the problem as a nonlinear fully discrete FD system, where the time derivative is discretized by the second-order backward difference formula (BDF) scheme, the Caputo fractional derivative is treated by means of \(L1\) discretization formula, and the spatial derivative is approximated by the central difference formula. For solving the nonlinear FD system more efficiently, a time two-grid algorithm is proposed, which consists of two steps: first, the nonlinear FD system on a coarse grid is solved by nonlinear iterations; second, the Newton iteration is utilized to solve the linearized FD system on the fine grid. The stability and convergence in \(L^2\)-norm are obtained for the two-grid FD scheme. Numerical results are consistent with the theoretical analysis. Meanwhile, numerical experiments show that the two-grid FD method is much more efficient than the general FD scheme for solving the nonlinear FD system.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65H10 | Numerical computation of solutions to systems of equations |
| 35R11 | Fractional partial differential equations |
| 26A33 | Fractional derivatives and integrals |
| 35Q49 | Transport equations |
Keywords:
two-grid algorithm; two-dimensional; nonlinear time-fractional mobile/immobile model; stability; convergence; numerical experimentsReferences:
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