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

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

doi: 10.21656/1000-0887.420172
  • 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
  • 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.

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