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

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

Year:    2019

Author:    Max Gunzburger, Jilu Wang

International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 225–239

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2019-IJNAM-12801

International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 225–239

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

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

Author Details

Max Gunzburger

Jilu Wang