14
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Implicit-Explicit difference schemes for nonlinear fractional differential equations with non-smooth solutions

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order \(0<\beta<1\). From the known structure of the non-smooth solution and by introducing corresponding correction terms, we can obtain uniformly second-order accuracy from these schemes. We prove the convergence and linear stability of the proposed schemes. Numerical examples illustrate the flexibility and efficiency of the IMEX schemes and show that they are effective for nonlinear and multi-rate fractional differential systems as well as multi-term fractional differential systems with non-smooth solutions.

          Related collections

          Most cited references39

          • Record: found
          • Abstract: not found
          • Article: not found

          Finite difference/spectral approximations for the time-fractional diffusion equation

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Detailed Error Analysis for a Fractional Adams Method

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              A Space-Time Spectral Method for the Time Fractional Diffusion Equation

                Bookmark

                Author and article information

                Journal
                2016-08-02
                Article
                1608.00831
                9ea4a2d4-0dc9-41d9-8cac-2930a57ccc0b

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                34A08, 35R11, 65L04, 65L05, 65L20, 65L70
                25 pages, 10 Postscript figures; accepted by SISC
                math.NA

                Numerical & Computational mathematics
                Numerical & Computational mathematics

                Comments

                Comment on this article