We present in this paper a unified framework for analyzing the spectral methods in
unbounded domains using mapped Jacobi, Laguerre and Hermite functions. A detailed …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

The time distributed-order diffusion-wave equation describes radial groundwater flow to or
from a well. In the paper, an alternating direction implicit (ADI) Legendre–Laguerre spectral …

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 …

Hierarchical model reduction is intended to solve efficiently partial differential equations in
domains with a geometrically dominant direction. In many engineering applications, these …

We extend the hierarchical model reduction procedure previously introduced in Ern et al.(in:
Kunisch, Of, Steinbach (eds) Numerical mathematics and advanced applications, Springer …

In this paper, we first introduce three series of Legendre rational basis functions on the
half/whole line by the diagonalization technique and the matrix decomposition technique …

In this paper, we introduce three series of Jacobi rational basis functions on the half line by
using the matrix decomposition technique. The new basis functions are simultaneously …

A triangular spectral element method is proposed for Stokes eigenvalues, which utilizes the
generalized orthogonal Koornwinder polynomials as the local basis functions. The local …