## How many steps still left to x*?

Abstract The high speed of $$x_{k}\rightarrow x^\ast\in{\mathbb R}$$ is usually measured using the C-, Q- or R-orders: \tag{$C$} \lim \frac…

## Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems

AbstractThe present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a…

## Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

AbstractIn this article, we present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow…

## Accurate spectral collocation computations of high order eigenvalues for singular Schrödinger equations-revisited

AbstractIn this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We…

## Accurate spectral collocation solutions to 2nd-order Sturm–Liouville problems

AbstractThis work is about the use of some classical spectral collocation methods as well as with the new software system…

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

AbstractWe are concerned with the study of some classical spectral collocation methods, mainly Chebyshev and sinc as well as with…

## 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 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 collocation based on quasi-classical orthogonal polynomials applied to solve a singular BVP from Hydrodynamics

AbstractIt is well established that spectral collocation methods based on classical orthogonal polynomials, in spite of their high order accuracy,…

## A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime

AbstractWe consider the numerical approximation of the ill-posed data assimilation problem for stationary convection–diffusion equations and extend our previous analysis…