Local convergence analysis of L1-ADI scheme for two-dimensional reaction-subdiffusion equation

Jiang, Yubing; Chen, Hu

doi:10.1007/s12190-024-02037-z

J. Appl. Math. Comput.

2024

DOI: 10.1007/s12190-024-02037-z

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Local convergence analysis of L1-ADI scheme for two-dimensional reaction-subdiffusion equation

Yubing Jiang,

Hu Chen

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2024

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A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations

2024

Z Angew Math Mech

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In the present paper, we derive a fast H3N3‐2‐based compact alternating direction implicit (ADI) scheme for the time fractional wave equation in two‐dimensional spatial domains. The time fractional derivative involved in the equation is discretized by the H3N3‐2 formula combined with sum‐of‐exponential technique. The former was first proposed by Du et al., while the latter has become a widely used technique to reduce the computational cost in the processing of convolution integrals. The spatial discretization adopts the standard compact ADI method, which can ensure that the space can reach the fourth‐order accuracy without increasing the amount of computation. The numerical stability and convergence of the difference scheme are analyzed rigorously. As an auxiliary illustration, a numerical example is given to verify the validity of the theoretical findings.

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A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations

2024

Z Angew Math Mech

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The High-Order ADI Difference Method and Extrapolation Method for Solving the Two-Dimensional Nonlinear Parabolic Evolution Equations

Shen,

Yang,

Zhang

2024

Mathematics

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In this paper, the numerical solution for two-dimensional nonlinear parabolic equations is studied using an alternating-direction implicit (ADI) Crank–Nicolson (CN) difference scheme. Firstly, we use the CN format in the time direction, and then use the CN format in the space direction before discretizing the second-order center difference quotient. In addition, we strictly prove that the proposed ADI difference scheme has unique solvability and is unconditionally stable and convergent. The extrapolation method is further applied to improve the numerical solution accuracy. Finally, two numerical examples are given to verify our theoretical results.

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Local convergence analysis of L1-ADI scheme for two-dimensional reaction-subdiffusion equation

Cited by 2 publications

References 18 publications

A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations

A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations

The High-Order ADI Difference Method and Extrapolation Method for Solving the Two-Dimensional Nonlinear Parabolic Evolution Equations

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