High-Order Numerical Methods for Solving Time Fractional Partial Differential EquationsReport as inadecuate




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Journal of Scientific Computing

, Volume 71, Issue 2, pp 785–803

First Online: 15 November 2016Received: 20 May 2016Revised: 23 October 2016Accepted: 02 November 2016DOI: 10.1007-s10915-016-0319-1

Cite this article as: Li, Z., Liang, Z. & Yan, Y. J Sci Comput 2017 71: 785. doi:10.1007-s10915-016-0319-1

Abstract

In this paper we introduce a new numerical method for solving time fractional partial differential equation. The time discretization is based on Diethelm’s method where the Hadamard finite-part integral is approximated by using the piecewise quadratic interpolation polynomials. The space discretization is based on the standard finite element method. The error estimates with the convergence order \O\tau ^{3-\alpha } + h^2, 0<\alpha <1\ are proved in detail by using the argument developed recently by Lv and Xu SIAM J Sci Comput 38:A2699–A2724, 2016, where \\tau \ and h denote the time and space step sizes, respectively. Numerical examples in both one- and two-dimensional cases are given.

KeywordsTime fractional partial differential equations Finite element method Error estimates Mathematics Subject Classification65M12 65M70 35S10 



Author: Zhiqiang Li - Zongqi Liang - Yubin Yan

Source: https://link.springer.com/







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