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 …

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 …

We present in this paper several extremely efficient and accurate spectral-Galerkin methods
for second-and fourth-order equations in polar and cylindrical geometries. These methods …

It is well known that for the discretization of the biharmonic operator with spectral methods
(Galerkin, tau, or collocation) we have a condition number of O (N8), where N is the number …

In this work, a Sinc-Galerkin method is considered and analyzed for solving the fourth-order
partial integro-differential equation with a weakly singular kernel. The time derivative and …

Contents: MOTIVATION--Non-linear elliptic equations in model problems; Linear algebraic
systems; Linear elliptic problems; Non-linear algebraic systems and preconditioning …

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 …

Spectral Methods for Differential Problems Page 1 Spectral Methods for Differential Problems
CI GHEORGHIU ”T. Popoviciu” Institute of Numerical Analysis, Cluj-Napoca, ROMANIA …

This article analyzes the solution of the integrated forms of fourth‐order elliptic differential
equations on a rectilinear domain using a spectral Galerkin method. The spatial …

We present a fast direct solver methodology for the Dirichlet biharmonic problem in a
rectangle. The solver is applicable in the case of the second order Stephenson scheme [JW …