Generalized Jacobi Rational Spectral Method and Its Applications

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...

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Bibliographic Details
Published in:Journal of scientific computing 2010-05, Vol.43 (2), p.201-238
Main Authors: Guo, Ben-Yu, Yi, Yong-Gang
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computation
Computational Mathematics and Numerical Analysis
Convergence
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Spectra
Spectral methods
Theoretical
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-010-9353-6