## The numerical approximation to positive solution for some reaction-diffusion problems

Abstract A one-dimensional reaction-diffusion problem, with the reaction term of the form $$u^{p}$$, $$p>1$$ is considered. For $$p=3$$, we deduce…

## Surface mobility of surfactant solutions XVI. Involvement of the fluid viscosities in the Marangoni flow – some aspects

AbstractThe influence of viscosity upon the Marangoni flow (induced by surface tension differences) in competition with the gravity flow, through…

## Numerical methods in establishment of concentration profile for the flows with chemical reactions over rotating disk

AbstractA viscous flow due to a rotating disk involving homogeneous as well as heterogeneous chemical reactions is considered. We simplify…

## On the bifurcation and variational approximation of the positive solution of a nonlinear reaction-diffusion problem

Abstract We consider a nonlinear, second-order, two-point boundary value problem that models some reaction-diffusion processes. When the reaction term has…

## On the use of Green’s formula for the solution of the Navier-Stokes equations

AbstractA general iterative procedure for solving Navier-Stokes system in stream function-vorticity variables  is considered. Using the fundamental solution for Laplace…

## 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…

## 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…

## Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: A comparative study

AbstractThis work deals with a comparison of different numerical schemes for the simulation of contaminant transport in heterogeneous porous media.…