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Generalized Jacobi rational spectral method on the half line. (English) Zbl 1259.65156
An orthogonal system on the half line, induced by generalized Jacobi functions is introduced. 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.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K65 Degenerate parabolic equations
41A20 Approximation by rational functions
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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