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Jacobi rational approximation and spectral method for differential equations of degenerate type


Authors: Zhong-qing Wang and Ben-yu Guo
Journal: Math. Comp. 77 (2008), 883-907
MSC (2000): Primary 41A20, 65M70, 35K65
DOI: https://doi.org/10.1090/S0025-5718-07-02074-1
Published electronically: November 19, 2007
MathSciNet review: 2373184
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Abstract: We introduce an orthogonal system on the half line, induced by Jacobi polynomials. Some results on the Jacobi rational approximation are established, which play important roles in designing and analyzing the Jacobi rational spectral method for various differential equations, with the coefficients degenerating at certain points and growing up at infinity. The Jacobi rational spectral method is proposed for a model problem appearing frequently in finance. Its convergence is proved. Numerical results demonstrate the efficiency of this new approach.


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Additional Information

Zhong-qing Wang
Affiliation: Department of Mathematics, Division of Computational Science of E-institute of Shanghai Universities, Shanghai Normal University, Shanghai, 200234, People’s Republic of China
Email: zqwang@shnu.edu.cn

Ben-yu Guo
Affiliation: Department of Mathematics, Division of Computational Science of E-institute of Shanghai Universities, Shanghai Normal University, Shanghai, 200234, People’s Republic of China
Email: byguo@shnu.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-07-02074-1
Keywords: Jacobi rational approximation, spectral method for differential equations of degenerate type on the half line, applications
Received by editor(s): March 15, 2006
Received by editor(s) in revised form: February 14, 2007
Published electronically: November 19, 2007
Additional Notes: The work of the authors was partially supported by NSF of China, N.10471095 and N.10771142, the National Basic Research Project No. 2005CB321701, SF of Shanghai, N.04JC14062, The Fund of Chinese Education Ministry, N.20040270002, Shanghai Leading Academic Discipline Project, N.T0401, and The Fund for E-institutes of Shanghai Universities, N.E03004
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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