Journal Article10.1007/S11075-019-00801-Y
A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model
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TL;DR: A time two-grid algorithm based on the finite difference (FD) method for the two-dimensional nonlinear time-fractional mobile/immobile transport model is proposed, which is much more efficient than the general FD scheme for solving the nonlinear FD system.
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Abstract: 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 L2-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.
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Citations
An alternating direction implicit Galerkin finite element method for the distributed-order time-fractional mobile–immobile equation in two dimensions
TL;DR: The alternating direction implicit (ADI) Galerkin finite element method (FEM) for solving the distributed-order time-fractional mobile–immobile equation in two dimensions and the stability and L 2 -norm convergence are proved.
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Time two-grid technique combined with temporal second order difference method for two-dimensional semilinear fractional sub-diffusion equations
Dakang Cen,Zhibo Wang +1 more
TL;DR: In this article , a high order difference scheme for two-dimensional semilinear fractional sub-diffusion equations was constructed and an efficient time two-grid algorithm was proposed to reduce the computation time.
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Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media
TL;DR: In this article , the authors presented an efficient numerical algorithm, which combines the fourth-order compact difference scheme (CDS) in space with the fast time two-mesh (TT-M) FBN- θ method, to solve the nonlinear distributed-order fractional Sobolev model appearing in porous media.
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An ADI compact difference scheme for the two-dimensional semilinear time-fractional mobile–immobile equation
TL;DR: An alternating direction implicit (ADI) compact difference scheme for solving semilinear time-fractional mobile–immobile equations in two dimensions is proposed and the accuracy and effectiveness of the scheme are illustrated by several numerical experiments.
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TL;DR: In this paper, a fractal mobile/immobile model for solute transport with power law waiting times in the immobile zone was proposed, leading to a fractional time derivative in the model equations, which captures the anomalous behavior of tracer plumes in heterogeneous aquifers.