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A High-Order Method with a Temporal Nonuniform Mesh for a Time-Fractional Benjamin–Bona–Mahony Equation
Lyu,Pin1,2; Vong,Seakweng2
2019-09-15
Source PublicationJournal of Scientific Computing
ISSN0885-7474
Volume80Issue:3Pages:1607-1628
AbstractThe solution of a time-fractional differential equation often exhibits a weak singularity near the initial time. It makes classical numerical methods with uniform mesh usually lose their accuracy. Technique of nonuniform mesh was found to be a very efficient approach in the literatures to recover the full accuracy based on reasonable regularity of the solution. In this paper, we study finite difference scheme with temporal nonuniform mesh for time-fractional Benjamin–Bona–Mahony equations with non-smooth solutions. Our approximation bases on an integral equation equivalent to the nonlinear problem under consideration. We employ high-order interpolation formulas to obtain a linearized scheme on a nonuniform mesh and, by using a modified Grönwall inequality established recently, we show that the proposed scheme with a temporal graded mesh is unconditionally third-order convergent in time with respect to discrete H-norm. Besides high order convergence the proposed scheme has the advantage that only linear systems are needed to be solved for obtaining approximated solutions. Numerical examples are provided to justify the accuracy.
KeywordCaputo derivative Graded mesh High-order method Nonuniform mesh Time-fractional nonlinear equation
DOI10.1007/s10915-019-00991-6
URLView the original
Language英語English
Scopus ID2-s2.0-85068110687
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Cited Times [WOS]:23   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorVong,Seakweng
Affiliation1.School of Economic Mathematics,Southwestern University of Finance and Economics,Chengdu,China
2.Department of Mathematics,University of Macau,Macao,Macao
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lyu,Pin,Vong,Seakweng. A High-Order Method with a Temporal Nonuniform Mesh for a Time-Fractional Benjamin–Bona–Mahony Equation[J]. Journal of Scientific Computing,2019,80(3):1607-1628.
APA Lyu,Pin,&Vong,Seakweng.(2019).A High-Order Method with a Temporal Nonuniform Mesh for a Time-Fractional Benjamin–Bona–Mahony Equation.Journal of Scientific Computing,80(3),1607-1628.
MLA Lyu,Pin,et al."A High-Order Method with a Temporal Nonuniform Mesh for a Time-Fractional Benjamin–Bona–Mahony Equation".Journal of Scientific Computing 80.3(2019):1607-1628.
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