Journal of Scientific Computing

, Volume 15, Issue 2, pp 117–147 | Cite as

A Rational Approximation and Its Applications to Differential Equations on the Half Line

  • Ben-Yu Guo
  • Jie Shen
  • Zhong-Qing Wang


An orthogonal system of rational functions is introduced. Some results on rational approximations based on various orthogonal projections and interpolations are established. These results form the mathematical foundation of the related spectral method and pseudospectral method for solving differential equations on the half line. The error estimates of the rational spectral method and rational pseudospectral method for two model problems are established. The numerical results agree well with the theoretical estimates and demonstrate the effectiveness of this approach.

legendre rational polynomials rational approximation spectral method pseudospectral method 


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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Ben-Yu Guo
    • 1
  • Jie Shen
    • 2
  • Zhong-Qing Wang
    • 3
  1. 1.School of Mathematical SciencesShangai Normal UniversityShanghaiPeople's Republic of China
  2. 2.Department of MathematicsPenn State University
  3. 3.Department of MathematicsShangai UniversityShangaiPeople's Republic of China

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