Journal of Scientific Computing

, Volume 27, Issue 1, pp 305–322

Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials


DOI: 10.1007/s10915-005-9055-7

Cite this article as:
Guo, BY., Shen, J. & Wang, LL. J Sci Comput (2006) 27: 305. doi:10.1007/s10915-005-9055-7


We extend the definition of the classical Jacobi polynomials withindexes α, β>−1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.


Generalized Jacobi polynomials spectral-Galerkin method high-order differential equations 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal University and Shanghai E-Institute for Computational SciencesShanghaiP. R. China
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA
  3. 3.Division of Mathematics, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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