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2006, Volume 6, Issue 6: 1381-1402. Doi: 10.3934/dcdsb.2006.6.1381
This issue Previous Article Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2)-equivariant systems Next Article Revisiting the slow manifold of the Lorenz-Krishnamurthy quintet

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

Received:  September 30, 2005
Revised:  May 31, 2006
Published:  October 2006
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 65M70, 35Q53; Secondary: 65M12.

    Citation:
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