Legendre-Laguerre coupled spectral element methods for second- and fourth-order equations on the half line (Q708283)

The authors propose some Legendre-Laguerre coupled spectral element method to solve numerically second and fourth-order equations on the half line. These methods are based on splitting the domain in two parts, then using the Legendre spectral element method in the finite subdomain and the Laguerre method in the infinite subdomain. An error analysis is investigated in order to establish the convergence of the method. An efficient computational process is introduced to solve the discrete system. Numerical examples are provided to ilustrate the theoretical results and the efficiency of the method.