Efficient Laguerre and Hermite Spectral Methods for Odd-Order Differential Equations in Unbounded Domains (Journal of Mathematical Study, 2020)
Laguerre dual-Petrov-Galerkin spectral methods and Hermite Galerkin spectral methods for solving odd-order differential equations in unbounded domains areproposed. Some Sobolev bi-orthogonal basis functions are constructed which lead tothe diagonalization of discrete systems. Numerical results demonstrate the effectiveness of the suggested approaches.
Keywords: Dual-Petrov-Galerkin spectral methods; Laguerre functions; Hermite functions; Sobolev bi-orthogonal functions; odd-order differential equations.