American Institute of Mathematical Sciences

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

 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.
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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