Generalized Jacobi Rational Spectral Method and Its Applications

Authors:
Ben-Yu Guo;Yong-Gang Yi
Affiliations:
Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, Shan ...;Department of Basic Courses, Tianhua College, Shanghai, China 201805
Venue:
Journal of Scientific Computing
Year:
2010

Citing 6
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Abstract

We introduce an orthogonal system on the whole line, induced by the generalized Jacobi functions. Some results on the generalized Jacobi rational approximation are established, which play important roles in the related spectral methods. As examples of applications, the rational spectral schemes are proposed for sine-Gordon, Klein-Gordon and Fisher equations, with the convergence analysis. Numerical results demonstrate their efficiency.