Generalized Jacobi rational spectral method on the half line

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.