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Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method
Author(s) -
Wei Leilei,
He Yinnian,
Tang Bo
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21756
Subject(s) - mathematics , discontinuous galerkin method , finite element method , partial differential equation , galerkin method , fractional calculus , space (punctuation) , integer (computer science) , order (exchange) , mathematical analysis , scheme (mathematics) , computer science , physics , finance , economics , thermodynamics , programming language , operating system
In this article, an implicit fully discrete local discontinuous Galerkin (LDG) finite element method, on the basis of finite difference method in time and LDG method in space, is applied to solve the time‐fractional Kawahara equation, which is introduced by replacing the integer‐order time derivatives with fractional derivatives. We prove that our scheme is unconditional stable and convergent through analysis. Extensive numerical results are provided to demonstrate the performance of the present method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013