American Institute of Mathematical Sciences

Advanced
November  2006, 6(6): 1381-1402. doi: 10.3934/dcdsb.2006.6.1381

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

Jie Shen 1, and  Li-Lian Wang 2,

1. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907
2. 

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore

Received  October 2005 Revised  June 2006 Published  August 2006

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.
Keywords: composite Legendre-Laguerre approximation, Dual-Petrov-Galerkin method, domain decomposition, KDV equation., Laguerre functions.
Mathematics Subject Classification: Primary: 65M70, 35Q53; Secondary: 65M1.
Citation: Jie Shen, Li-Lian Wang. Laguerre and composite Legendre-Laguerre Dual-Petrov-Galerkin methods for third-order equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1381-1402. doi: 10.3934/dcdsb.2006.6.1381
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