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On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations

Author

Listed:
  • Junjiang Lai

    (College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China)

  • Hongyu Liu

    (Department of Mathematics, City University of Hong Kong, Hong Kong, China)

Abstract

In this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose a Galerkin finite element scheme for both the temporal and spatial discretizations. For the proposed numerical scheme, we derive sharp stability estimates as well as optimal a priori error estimates. Extensive numerical experiments are conducted to verify the promising features of the newly proposed method.

Suggested Citation

  • Junjiang Lai & Hongyu Liu, 2021. "On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:2014-:d:620153
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