Advances in Computational Mathematics

, Volume 32, Issue 4, pp 393–429

Composite Laguerre-Legendre spectral method for exterior problems



In this paper, we propose a composite Laguerre-Legendre spectral method for two-dimensional exterior problems. Results on the composite Laguerre-Legendre approximation, which is a set of piecewise mixed approximations coupled with domain decomposition, are established. These results play important roles in the related spectral methods for exterior problems. As examples of applications, the composite spectral schemes are provided for two model problems, with the convergence analysis. An efficient implementation is described. Numerical results demonstrate the spectral accuracy in space of this new approach, and confirm the analysis. The approximation results and techniques developed in this paper are also applicable to other problems defined on unbounded domains.


Composite Laguerre-Legendre spectral method Exterior problems 

Mathematics Subject Classifications (2000)

65M70 41A30 35J20 35K20 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Scientific Computing Key Laboratory of Shanghai UniversitiesShanghai UniversityShanghaiChina
  3. 3.Division of Computational Science of E-Institute of Shanghai UniversitiesShanghai UniversityShanghaiChina
  4. 4.Department of Mathematics and PhysicsHenan University of Science and TechnologyLuoYangChina

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