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 …

Completely revised text focuses on use of spectral methods to solve boundary value,
eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational …

This book expands lecture notes by the authors for a course on Introduction of Spectral
Methods taught in the past few years at Penn State University, Simon Fraser University, the …

In this paper we propose a collocation method for solving some well-known classes of Lane–
Emden type equations which are nonlinear ordinary differential equations on the semi …

Hermite spectral methods are investigated for linear diffusion equations and nonlinear
convection-diffusion equations in unbounded domains. When the solution domain is …

We discuss the numerical treatment of a nonlinear second order boundary value problem in
ordinary differential equations posed on an unbounded domain which represents the …

We discuss numerical methods for the computation and continuation of equilibria and
bifurcation points of equilibria of dynamical systems. We further consider the computation of …

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation
approach to solve Volterra's model for population growth of a species within a closed …

Based on a new approximation method, namely pseudospectral method, a solution for the
three order nonlinear ordinary differential laminar boundary layer Falkner–Skan equation …