Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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FAST MATRIX SPLITTING ITERATION METHOD FOR THE LINEAR SYSTEM FROM SPATIAL FRACTIONAL DIFFUSION EQUATIONS

  • LIANG, YUPENG (Department of Mathematics, Northeastern University) ;
  • SHAO, XINHUI (Department of Mathematics, College of Sciences, Northeastern University)
  • Received : 2020.05.27
  • Accepted : 2020.07.10
  • Published : 2020.09.30
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Abstract

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.

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