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High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations
Li, Zhiqiang Liang, Zongqi Yan, Yubin
Li, Zhiqiang
Liang, Zongqi
Yan, Yubin
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Publication Date
2016-11-15
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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(τ^(3−α) +h^2 ),0<α<1
O(τ^(3−α)+h^2),0<α<1
are proved in detail by using the argument developed recently by Lv and Xu (SIAM J Sci Comput 38:A2699–A2724, 2016), where τ and h denote the time and space step sizes, respectively. Numerical examples in both one- and two-dimensional cases are given.
Citation
Li, Z., Liang, Z. & Yan, Y. (2017). High-order numerical methods for solving time fractional partial differential equations. Journal of Scientific Computing, 71(2), 785-803. DOI: 10.1007/s10915-016-0319-1
Publisher
Springer
Journal
Journal of Scientific Computing
Research Unit
DOI
10.1007/s10915-016-0319-1
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PubMed Central ID
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Article
Language
en
Description
The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-016-0319-1
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ISSN
0885-7474
EISSN
1573-7691