Laguerre and composite Legendre-Laguerre Dual-Petrov-Galerkin methods for third-order equations | Zendy

Jie Shen | Zendy; Li-Lian Wang | Zendy

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Laguerre and composite Legendre-Laguerre Dual-Petrov-Galerkin methods for third-order equations

Author(s) -

Jie Shen,

Li-Lian Wang

Publication year - 2006

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2006.6.1381

Subject(s) - laguerre polynomials , petrov–galerkin method , mathematics , legendre polynomials , laguerre's method , galerkin method , legendre wavelet , basis function , mathematical analysis , dual (grammatical number) , legendre's equation , orthogonal polynomials , finite element method , classical orthogonal polynomials , computer science , physics , wavelet , discrete wavelet transform , art , wavelet transform , literature , artificial intelligence , thermodynamics

Dual-Petrov-Galerkin approximations to linear third-order equations and the Korteweg-de Vries equation on semi-infinite intervals are considered. It is shown that by choosing appropriate trial and test basis functions the Dual-Petrov-Galerkin method using Laguerre functions leads to strongly coercive linear systems which are easily invertible and enjoy optimal convergence rates. A novel multi-domain composite Legendre-Laguerre dual-Petrov-Galerkin method is also proposed and implemented. Numerical results illustrating the superior accuracy and effectiveness of the proposed dual-Petrov-Galerkin methods are presented.

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