A Second-Order Crank-Nicolson Method for Time-Fractional PDEs

Authors

  • Max Gunzburger Department of Scientific Computing, Florida State University, Tallahassee, FL 32304, USA
  • Jilu Wang Department of Mathematics and Statistics, Mississippi State University, Starkville, MS 39762, USA

Keywords:

Crank-Nicolson scheme, time-fractional equation, convolution quadrature, finite element method, error estimates.

Abstract

Based on convolution quadrature in time and continuous piecewise linear finite element approximation in space, a Crank-Nicolson type method is proposed for solving a partial differential equation involving a fractional time derivative. The method achieves second-order convergence in time without being corrected at the initial steps. Optimal-order error estimates are derived under regularity assumptions on the source and initial data but without having to assume regularity of the solution.

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Published

2019-02-22

Issue

Vol. 16 No. 2 (2019)

Section

Articles