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Jacobi rational approximation and spectral method for differential equations of degenerate type |
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| Authors: | Zhong-qing Wang 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 ; Department of Mathematics, Division of Computational Science of E-institute of Shanghai Universities, Shanghai Normal University, Shanghai, 200234, People's Republic of China |
| 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. |
| Keywords: | Jacobi rational approximation spectral method for differential equations of degenerate type on the half line applications |
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