Advances in Computational Mathematics

, Volume 28, Issue 3, pp 237–267 | Cite as

Irrational approximations and their applications to partial differential equations in exterior domains,

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Abstract

A family of orthogonal systems of irrational functions on the semi-infinite interval is introduced. The proposed orthogonal systems are based on Jacobi polynomials through an irrational coordinate transform. This family of orthogonal systems offers great flexibility to match a wide range of asymptotic behaviors at infinity. Approximation errors by the basic orthogonal projection and various other orthogonal projections related to partial differential equations in unbounded domains are established. As an example of applications, a Galerkin approximation using the proposed irrational functions to an exterior problem is analyzed and implemented. Numerical results in agreement with our theoretical estimates are presented.

Keywords

rational and irrational functions spectral method semi-infinite interval exterior problems 

Mathematics Subject Classifications (2000)

65N35 65N22 65F05 41A20 
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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal University and Shanghai E-Institute for Computational ScienceShanghaiChina
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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