In this paper, we review some results on the spectral methods. We first consider the Jacobi
spectral method and the generalized Jacobi spectral method for various problems, including …

We provide an overview of matrix decomposition algorithms (MDAs) for the solution of
systems of linear equations arising when various discretization techniques are applied in the …

A fully diagonalized spectral method using generalized Laguerre functions is proposed and
analyzed for solving elliptic equations on the half line. We first define the generalized …

Mitigating the impact of waves leaving a numerical domain has been a persistent challenge
in numerical modeling. Reducing wave reflection at the domain boundary is crucial for …

We introduce an extended discontinuous Galerkin discretization of hyperbolic–parabolic
problems on multidimensional semi‐infinite domains. Building on previous work on the one …

Based on the generalized matrix eigenvalue decomposition technique, two kinds of basis
functions are constructed, which are simultaneously orthogonal in both L 2-and H 1-inner …

We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization
of advection–diffusion equations on semi-infinite domains. The semi-infinite half line is split …

In this paper, we propose a Fourier-Laguerre spectral method for exterior problems of two-
dimensional complex obstacles based on the mapping method. We first use a polar …

Mitigating the impact of waves leaving a numerical domain has been a persistent challenge
in numerical modeling. Reducing wave reflection at the domain boundary is crucial for …

将比例边界坐标插值方法引入谱元法, 构成比例边界谱单元, 对无穷域Euler 方程进行数值模拟.
阐述了比例边界谱单元的基本使用方法以及基于比例边界谱元的Runge-Kutta 间断Galerkin …