NUMERICAL ANALYSIS OF THE FRACTIONAL SEVENTH-ORDER KDV EQUATION USING AN IMPLICIT FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD
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Wei, Leilei
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Xi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R ChinaXi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China
Wei, Leilei
[1
]
He, Yinnian
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Xi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R ChinaXi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China
He, Yinnian
[1
]
Zhang, Yan
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Univ Paris 06, UMR 7598, CNRS, Lab Jacques Louis Lions, F-75005 Paris, FranceXi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China
Zhang, Yan
[2
]
机构:
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China
[2] Univ Paris 06, UMR 7598, CNRS, Lab Jacques Louis Lions, F-75005 Paris, France
In this paper an implicit fully discrete local discontinuous Galerkin (LDG) finite element method is applied to solve the time-fractional seventh-order Korteweg-de Vries (sKdV) equation, which is introduced by replacing the integer-order time derivatives with fractional derivatives. We prove that our scheme is unconditional stable and L-2 error estimate for the linear case with the convergence rate O(h(k+1) + (Delta t)(2) + (Delta t)(alpha/2) h(k+1/2)) through analysis. Extensive numerical results are provided to demonstrate the performance of the present method.
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页码:430 / 444
页数:15
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[1]
[Anonymous], 2006, THEORY APPL FRACTION, DOI DOI 10.1016/S0304-0208(06)80001-0
机构:
Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
Jimei Univ, Coll Math, Xiamen 361021, Peoples R ChinaQueensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
Chen, J.
Liu, F.
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Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
S China Univ Technol, Sch Math Sci, Guangzhou 510640, Peoples R ChinaQueensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
Liu, F.
Anh, V.
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Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, AustraliaQueensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
机构:
Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
Jimei Univ, Coll Math, Xiamen 361021, Peoples R ChinaQueensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
Chen, J.
Liu, F.
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机构:
Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
S China Univ Technol, Sch Math Sci, Guangzhou 510640, Peoples R ChinaQueensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
Liu, F.
Anh, V.
论文数: 0引用数: 0
h-index: 0
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Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, AustraliaQueensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia