Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation

  • Ben-yu Guo
  • Jie Shen
  • Cheng-long Xu


We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods.

Hermite approximation Dirac equation spectral and pseudospectral 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Ben-yu Guo
    • 1
  • Jie Shen
    • 2
    • 3
  • Cheng-long Xu
    • 4
  1. 1.School of Mathematical SciencesShanghai Normal UniversityShanghaiP.R. China
  2. 2.Department of MathematicsXiamen UniversityXiamenP.R. China
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA
  4. 4.Department of Applied MathematicsTongji UniversityShanghaiP.R. China

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