Mixed Generalized Laguerre-Legendre Approximation and Its Applications

In this paper, we propose mixed generalized Laguerre-Legendre spectral method for partial differential equation set in a semiinfinite channel. We investigate mixed generalized Laguerre-Legendre approximation. We propose the new algorithm for various boundary condition problems. The global convergence of proposed algorithms are proved. Numerical results demonstrate the spectral accuracy of these new approaches and coincide well with theoretical analysis.