Exponential integrators for time-fractional partial differential equations

被引：23
|
作者：
Garrappa, R. [1 ]
机构：
[1] Univ Bari, Dipartimento Matemat, I-70125 Bari, Italy
来源：
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS | 2013年 / 222卷 / 08期
关键词：
MULTISTEP METHODS; MATRIX; APPROXIMATIONS; DIFFUSION; ERROR; VOLTERRA;
D O I：
10.1140/epjst/e2013-01973-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Time-fractional partial differential equations can be numerically solved by first discretizing with respect to the spatial derivatives and hence applying a time-step integrator. An exponential integrator for fractional differential equations is proposed to overcome the stability issues due to the stiffness in the resulting semi-discrete system. Convergence properties and the main implementation issues are studied. The advantages of the proposed method are illustrated by means of some test problems.
引用
收藏
页码：1915 / 1927
页数：13
相关论文
共 50 条
  • [31] AN ITERATIVE METHOD FOR SOLVING TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS WITH PROPORTIONAL DELAYS
    Mallick, B.
    Sahu, P. K.
    Routaray, M.
    [J]. TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2023, 13 (01): : 74 - 85
  • [32] Local symmetry structure and potential symmetries of time-fractional partial differential equations
    Zhang, Zhi-Yong
    Lin, Zhi-Xiang
    [J]. STUDIES IN APPLIED MATHEMATICS, 2021, 147 (01) : 363 - 389
  • [33] Solitary wave solutions for some nonlinear time-fractional partial differential equations
    S Z Hassan
    Mahmoud A E Abdelrahman
    [J]. Pramana, 2018, 91
  • [34] Solitary wave solutions for some nonlinear time-fractional partial differential equations
    Hassan, S. Z.
    Abdelrahman, Mahmoud A. E.
    [J]. PRAMANA-JOURNAL OF PHYSICS, 2018, 91 (05):
  • [35] A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
    Liu, Yang
    Li, Hong
    Gao, Wei
    He, Siriguleng
    Fang, Zhichao
    [J]. SCIENTIFIC WORLD JOURNAL, 2014,
  • [36] Exact solution of time-fractional partial differential equations using sumudu transform
    Karbalaie, Abdolamir
    Montazeri, Mohammad Mehdi
    Muhammed, Hamed Hamid
    [J]. WSEAS Transactions on Mathematics, 2014, 13 (01) : 142 - 151
  • [37] A SOBOLEV SPACE THEORY FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME-FRACTIONAL DERIVATIVES
    Kim, Ildoo
    Kim, Kyeong-Hun
    Lim, Sungbin
    [J]. ANNALS OF PROBABILITY, 2019, 47 (04): : 2087 - 2139
  • [38] Numerical solution of time-fractional fourth-order partial differential equations
    Siddiqi, Shahid S.
    Arshed, Saima
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2015, 92 (07) : 1496 - 1518
  • [39] Symmetry structure of multi-dimensional time-fractional partial differential equations
    Zhang, Zhi-Yong
    Zheng, Jia
    [J]. NONLINEARITY, 2021, 34 (08) : 5186 - 5212
  • [40] QUASI-LINEAR (STOCHASTIC) PARTIAL DIFFERENTIAL EQUATIONS WITH TIME-FRACTIONAL DERIVATIVES
    Liu, Wei
    Roeckner, Michael
    da Silva, Jose Luis
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2018, 50 (03) : 2588 - 2607
12345