A fast linearized numerical method for nonlinear time-fractional diffusion equations
Lyu,Pin1; Vong,Seakweng2
Source PublicationNumerical Algorithms
AbstractIn this paper, we study a fast linearized numerical method for solving nonlinear time-fractional diffusion equations. A new weighted method is proposed to construct linearized approximation, which enables the unconditional convergence to be established when the nonlinearity f(u) is only locally Lipschitz continuous. In order to reduce the computational cost, the sum-of-exponentials (SOE) technique is employed to evaluate the kernel function in the Caputo derivative. By using the complementary discrete kernels for the coefficients of the refined fast weighted discretization, the proposed method is shown to be unconditionally convergent with respect to the discrete H-norm. The fast linearized method can also be extended to nonlinear multi-term and distributed-order time-fractional diffusion equations. Numerical examples with different types of nonlinear functions are provided to demonstrate the behavior of proposed methods for both smooth and weakly singular solutions.
KeywordCaputo derivative Linearized method Nonlinear time-fractional diffusion equation
URLView the original
Scopus ID2-s2.0-85088480344
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorVong,Seakweng
Affiliation1.School of Economic Mathematics,Southwestern University of Finance and Economics,Chengdu,China
2.Department of Mathematics,University of Macau,Macao,China
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lyu,Pin,Vong,Seakweng. A fast linearized numerical method for nonlinear time-fractional diffusion equations[J]. Numerical Algorithms,2020.
APA Lyu,Pin,&Vong,Seakweng.(2020).A fast linearized numerical method for nonlinear time-fractional diffusion equations.Numerical Algorithms.
MLA Lyu,Pin,et al."A fast linearized numerical method for nonlinear time-fractional diffusion equations".Numerical Algorithms (2020).
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