# (original)

## On the existence and uniqueness of positive solutions of some mildly nonlinear elliptic boundary value problems

AbstractFor a homogeneous Dirichlet problem attached to a semilinear elliptic equation we study the existence and uniqueness of non-negative solutions.…

## On the Chebyshev-tau approximation for some singularly perturbed two point boundary value problems – Numerical experiments

AbstractIn this paper we are concerned with numerical stability of Chebyshev-tau method in solving some singularly perturbed two-point boundary value…

## A unified treatment of boundary layer and lubrication approximations in viscous fluid mechanics

AbstractIt is a matter of every day experience to find the boundary layer and lubrication approximations exposed as if they…

## On the flow of a viscous thin layer on an inclined solid plane driven by a constant surface tension gradient

AbstractSteady flow of a thin layer (trickle, rivulet) of viscous fluid down an inclined surface is considered, via a thin-film…

## Spectral collocation solutions to systems of boundary layer type

AbstractThree spectral collocation methods, namely Laguerre collocation (LC), Laguerre Gauss Radau collocation (LGRC) and mapped Chebyshev collocation (ChC) are used…

## All roots spectral methods: Constraints, floating point arithmetic and root exclusion

Abstract The nonlinear two-point boundary value problem (TPBVP for short) $u_{xx}+u^{3}=0,\quad u(0)=u(1)=0,$ offers several insights into spectral methods. First, it…

## Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. Part II. Indirect approximation

AbstractIn this paper, we continue the study initiated in our previous work [3] and design a projection-like algorithm to approximate…

## Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. Part I. Direct (variational) approximation

AbstractPublisher NameWe consider a nonlinear, second-order, two-point boundary value problem that models some reaction-diffusion precesses. When the reaction term has…

## On some one-step implicit methods as dynamical systems

AbstractThe one-step implicit methods, the backward Euler being the most known, require the solution of a nonlinear equation at each…

## On the accuracy of Stoermer/Verlet method as the numerical integrator of the n-body problem – Application to solar system

AbstractThe Newton-Störmer/Verlet-leapfrog method (S/V) is a symplectic and symmetric one of order two, which, when applied to separable Hamiltonian dynamical systems,…