On the behavior of a thin liquid layer flowing due to gravity and a surface tension gradient
AbstractA thin liquid layer flowing due to gravity and a surface tension gradient are taken into account. On the liquid/gas…
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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 spectral properties of some Chebyshev-type methods. Dimension vs. structure
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
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…
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…