Jacobi rational approximation and spectral method for differential equations of degenerate type
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- by Zhong-qing Wang and Ben-yu Guo;
- Math. Comp. 77 (2008), 883-907
- DOI: https://doi.org/10.1090/S0025-5718-07-02074-1
- Published electronically: November 19, 2007
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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.References
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Bibliographic 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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 883-907
- MSC (2000): Primary 41A20, 65M70, 35K65
- DOI: https://doi.org/10.1090/S0025-5718-07-02074-1
- MathSciNet review: 2373184