A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

Yong-LiangZhao, global

doi:10.4208/eajam.200618.250319

Cited by 3 publications

(1 citation statement)

References 48 publications

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“…e scheme is unconditional stabile and convergent. For a class of onedimensional and two-dimensional time FRDE with variable coefficients and time drift term, Zhao and Gu [19] presented an implicit finite difference scheme based on the L2 − 1 σ formula. e unconditional stability and convergence of this scheme are proved rigorously by the discrete energy method, and the optimal convergence order in the L2 − norm is O(τ 2 + h 2 ).…”

Section: Introductionmentioning

confidence: 99%

An Efficient Parallel Approximate Algorithm for Solving Time Fractional Reaction-Diffusion Equations

Yang

2020

Mathematical Problems in Engineering

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In this paper, we construct pure alternative segment explicit-implicit (PASE-I) and implicit-explicit (PASI-E) difference algorithms for time fractional reaction-diffusion equations (FRDEs). They are a kind of difference schemes with intrinsic parallelism and based on classical explicit scheme and classical implicit scheme combined with alternating segment technology. The existence and uniqueness analysis of solutions of the parallel difference schemes are given. Both the theoretical proof and the numerical experiment show that PASE-I and PASI-E schemes are unconditionally stable and convergent with second-order spatial accuracy and 2−α order time accuracy. Compared with implicit scheme and E-I (I-E) scheme, the computational efficiency of PASE-I and PASI-E schemes is greatly improved. PASE-I and PASI-E schemes have obvious parallel computing properties, which shows that the difference schemes with intrinsic parallelism in this paper are feasible to solve the time FRDEs.

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Section: Introductionmentioning

confidence: 99%

An Efficient Parallel Approximate Algorithm for Solving Time Fractional Reaction-Diffusion Equations

Yang

2020

Mathematical Problems in Engineering

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Fast and high-order difference schemes for the fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions

Ran

Luo

2021

Mathematics and Computers in Simulation

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Galerkin spectral method for a multi-term time-fractional diffusion equation and an application to inverse source problem

Sun¹,

Chang²

2022

NHM

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<abstract><p>In this paper, we employ the Galerkin spectral method to handle a multi-term time-fractional diffusion equation, and investigate the numerical stability and convergence of the proposed method. In addition, we find an interesting application of the Galerkin spectral method to solving an inverse source problem efficiently from the noisy final data in a general bounded domain, and the uniqueness and the ill-posedness for the inverse problem are proved based on expression of the solution. Furthermore, we compare the calculation results of spectral method and finite difference method without any regularization method, and get a norm estimate of the coefficient matrix of a spectral method discretized. And for that we conclude that the spectral method itself can act as a regularization method for some inverse problem (such as inverse source problem). Finally, several numerical examples are used to illustrate the effectiveness and accuracy of the method.</p></abstract>

show abstract

A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

Cited by 3 publications

References 48 publications

An Efficient Parallel Approximate Algorithm for Solving Time Fractional Reaction-Diffusion Equations

An Efficient Parallel Approximate Algorithm for Solving Time Fractional Reaction-Diffusion Equations

Fast and high-order difference schemes for the fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions

Galerkin spectral method for a multi-term time-fractional diffusion equation and an application to inverse source problem

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