TY - JOUR T1 - Efficient Laguerre and Hermite Spectral Methods for Odd-Order Differential Equations in Unbounded Domains AU - Xu , Cheng AU - Yu , Xuhong AU - Wang , Zhongqing JO - Journal of Mathematical Study VL - 2 SP - 192 EP - 211 PY - 2020 DA - 2020/05 SN - 53 DO - http://doi.org/10.4208/jms.v53n2.20.04 UR - https://global-sci.org/intro/article_detail/jms/16804.html KW - Dual-Petrov-Galerkin spectral methods, Laguerre functions, Hermite functions, Sobolev bi-orthogonal functions, odd-order differential equations. AB -
Laguerre dual-Petrov-Galerkin spectral methods and Hermite Galerkin spectral methods for solving odd-order differential equations in unbounded domains are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Numerical results demonstrate the effectiveness of the suggested approaches.