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

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

On spectral properties of some Chebyshev-type methods. Dimension vs. structure

7 years ago
AbstractThe aim of the present paper is to analyze the non-normality of the matrices (finite dimensional operators) which result when some…

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

7 years ago
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

7 years ago
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

7 years ago
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

7 years ago
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

7 years ago
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

7 years ago
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

7 years ago
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

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