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A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave Equations
Lyu, Pin1; Vong, Seakweng2
2022-10-01
Source PublicationJournal of Scientific Computing
ISSN0885-7474
Volume93Issue:1
Abstract

We introduce a symmetric fractional-order reduction (SFOR) method to construct numerical algorithms on general nonuniform temporal meshes for semilinear fractional diffusion-wave equations. By using the novel order reduction method, the governing problem is transformed to an equivalent coupled system, where the explicit orders of time-fractional derivatives involved are all α/ 2 (1 < α< 2). The linearized L1 scheme and Alikhanov scheme are then proposed on general time meshes. Under some reasonable regularity assumptions and weak restrictions on meshes, the optimal convergence is derived for the two kinds of difference schemes by H energy method. An adaptive time stepping strategy which based on the (fast linearized) L1 and Alikhanov algorithms is designed for the semilinear diffusion-wave equations. Numerical examples are provided to confirm the accuracy and efficiency of proposed algorithms.

KeywordAdaptive Mesh Diffusion-wave Equation Nonuniform Mesh Weak Singularity
DOI10.1007/s10915-022-02000-9
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000853857600001
Scopus ID2-s2.0-85139396743
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.School of Mathematics, Southwestern University of Finance and Economics, Chengdu, China
2.Department of Mathematics, University of Macau, Macao
Recommended Citation
GB/T 7714
Lyu, Pin,Vong, Seakweng. A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave Equations[J]. Journal of Scientific Computing,2022,93(1).
APA Lyu, Pin,&Vong, Seakweng.(2022).A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave Equations.Journal of Scientific Computing,93(1).
MLA Lyu, Pin,et al."A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave Equations".Journal of Scientific Computing 93.1(2022).
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