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…
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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,…
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…
Accurate numerical solutions to stationary free surface problems from capillarity
AbstractThe paper considers two static problems from capillarity. The first one consists in the determination of the surface of a…