Abstract
We introduce an orthogonal system on the half line, induced by generalized Jacobi functions. Some basic results on the generalized Jacobi rational approximation are established, which play important roles in the related spectral method. As an example of applications, the rational spectral method is proposed for partial differential equations of degenerate type. Its convergence is proved. Numerical results demonstrate its efficiency.
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Communicated by Zhongying Chen.
This work is supported in part by NSF of China N. 11171227, Fund for Doctor Authority of Chinese Educational Ministry No. 20080270001, Shanghai Leading Academic Discipline Project No. S30405, Fund for E-institute of Shanghai Universities No. E03004, and Fund for Excellent Young Teachers of Shanghai Universities No. THC10020.
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Yi, Yg., Guo, By. Generalized Jacobi rational spectral method on the half line . Adv Comput Math 37, 1–37 (2012). https://doi.org/10.1007/s10444-011-9193-4
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DOI: https://doi.org/10.1007/s10444-011-9193-4