Pointwise-in-time error estimate of an ADI scheme for two-dimensional multi-term subdiffusion equation

Cao, Dewei; Chen, Hu

doi:10.1007/s12190-022-01759-2

Cited by 10 publications

(1 citation statement)

References 23 publications

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“…Due to these advantages, the ADI algorithm is favored by many scholars, thus a large number of related researches have emerged, for example, ADI finite element methods [8, 23], ADI finite difference methods [17‐20], ADI finite volume methods [27, 38], and so on. In addition, some scholars have proposed ADI method for solving multi‐term diffusion equations [2, 9]. These researches encourage and inspire our next work.…”

Section: Introductionmentioning

confidence: 84%

Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels

Zhao,

Chen,

2023

Numerical Methods Partial

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This work develops two temporal second‐order alternating direction implicit (ADI) numerical schemes for solving multidimensional parabolic‐type integrodifferential equations with multi‐term weakly singular Abel kernels. For the two‐dimensional (2D) case, applying the Crank–Nicolson method and product integration rule to discretizations of temporal derivative and integral terms, respectively, and the spatial discretization is proposed using a compact difference formulation combined with the ADI algorithm; for the three‐dimensional case, the method of temporal discretization is the same as the 2D case, and then we employ the standard finite difference in space to construct a fully discrete ADI finite difference scheme. The ADI technique is used to reduce the calculation cost of the high‐dimensional problem. Besides, the stability and convergence of two ADI schemes are rigorously proved by the energy argument, in which the first scheme converges to the order , where , , and denote the time‐space step sizes, respectively, and the second scheme converges to the space‐time second‐order accuracy. Finally, the numerical results verify the correctness of the theoretical analysis and show that the method of this article is competitive with the existing research work.

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Section: Introductionmentioning

confidence: 84%

Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels

Zhao,

Chen,

2023

Numerical Methods Partial

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Error estimate of GL‐ADI scheme for 2D multiterm nonlinear time‐fractional subdiffusion equation

Jiang,

Chen

2024

Math Methods in App Sciences

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In this paper, a 2D multiterm nonlinear problem of the form is considered, where each Caputo fractional derivative is of order . We use the Grünwald–Letnikov(GL) scheme on uniform mesh to discretize the multiterm Caputo fractional derivative and finite difference scheme is used for spatial discretization, and then we construct a fully discrete GL‐ADI scheme. A discrete Gronwall inequality is introduced for getting the sharp pointwise‐in‐time error estimate on uniform mesh. Numerical examples are provided to verify the sharpness of our error estimate.

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Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation

Jiang,

Chen

2024

Numerical Methods Partial

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In this paper, we consider the numerical approximation for a two‐dimensional multiterm reaction‐subdiffusion equation, where we adopt an alternating direction implicit (ADI) method combined with the L1 approximation for the multiterm time Caputo fractional derivatives of orders between 0 and 1. Stability and convergence of the full‐discrete L1‐ADI scheme are established. The final convergence in time direction is point‐wise, that is, at . Numerical results are given to confirm our theoretical results.

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Pointwise-in-time error estimate of an ADI scheme for two-dimensional multi-term subdiffusion equation

Cited by 10 publications

References 23 publications

Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels

Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels

Error estimate of GL‐ADI scheme for 2D multiterm nonlinear time‐fractional subdiffusion equation

Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation

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