An Element-Free Galerkin Method for Time-Fractional Diffusion-Wave Equations

WU Di; LI Xiaolin

doi:10.21656/1000-0887.420172

Volume 43 Issue 2

Feb. 2022

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WU Di, LI Xiaolin. An Element-Free Galerkin Method for Time-Fractional Diffusion-Wave Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 215-223. doi: 10.21656/1000-0887.420172

Citation:

WU Di, LI Xiaolin. An Element-Free Galerkin Method for Time-Fractional Diffusion-Wave Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 215-223. doi: 10.21656/1000-0887.420172

Citation:

WU Di, LI Xiaolin. An Element-Free Galerkin Method for Time-Fractional Diffusion-Wave Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 215-223. doi: 10.21656/1000-0887.420172

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An Element-Free Galerkin Method for Time-Fractional Diffusion-Wave Equations

doi: 10.21656/1000-0887.420172

WU Di,
LI Xiaolin^,

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China

Received Date: 2021-06-23
Accepted Date: 2021-06-23
Rev Recd Date: 2021-08-27

Available Online: 2022-01-07

Publish Date: 2022-02-01

Abstract

Abstract

Numerical solution and theoretical error analysis of the element-free Galerkin (EFG) method were presented for the time-fractional diffusion-wave equations in the sense of Caputo. Through discretization of the time variables in the equation with the L1 approximate formula, the time-fractional diffusion-wave equation was transformed into a series of time-independent integer-order differential equations. Then, the penalty method was used to deal with the Dirichlet boundary condition and the EFG method was used to discretize the integer-order differential equations. Error estimates of the EFG method for the time-fractional diffusion-wave equations were derived theoretically. Finally, several numerical examples show the accuracy and effectiveness of the proposed meshless method.
- time-fractional diffusion-wave equation,
- element-free Galerkin method,
- L1 approximation formula,
- error estimation

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References(18)

References

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