## Spectral collocation solutions to second order singular Sturm-Liouville eigenproblems

AbstractWe comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the…

## Accurate spectral collocation computation of high order eigenvalues for singular Schrödinger equations

AbstractWe are concerned with the study of some classical spectral collocation methods as well as with the new software system…

## Accurate spectral collocation solutions to some Bratu’s type Boundary Value Problems

AbstractWe solve by Chebyshev spectral collocation some genuinely nonlinear Liouville-Bratu-Gelfand type, 1D and a 2D boundary value problems. The problems…

## Spectral Methods for Non-Standard Eigenvalue Problems. Fluid and Structural Mechanics and Beyond

Book summarySummary of the book… Book titleSpectral Methods for Non-Standard Eigenvalue Problems Book subtitleFluid and Structural Mechanics and Beyond Book…

## Methods of Newton and Newton-Krylov type

Book summaryLocal convergence results on Newton-type methods for nonlinear systems of equations are studied. Solving of large linear systems by…

## A Chebyshev-Galerkin method for fourth order problems

AbstractWe study the linear stability of some Marangoni flows (thin films) on an inclined plane. The Orr-Sommerfeld eigenproblem contains two…

## Spectral methods in linear stability. Applications to thermal convection with variable gravity field

AbstractThe onset of convection in a horizontal layer of fluid heated from below in the presence of a gravity field…

## On the numerical treatment of the eigenparameter dependent boundary conditions

AbstractIn this paper, we consider the numerical treatment of singular eigenvalue problems supplied with eigenparameter dependent boundary conditions using spectral…

## On a third order iterative method for solving polynomial operator equations

Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…

## On approximating the eigenvalues and eigenvectors of linear continuous operators

Abstract We consider the computing of an eigenpair (an eigenvector $$v=(v^{(i)})_{i=1,n}$$ and an eigenvalue $$\lambda$$) of a matrix $$A\in\mathbb{R}^{n\times n}$$, by…