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…
works
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,…
On the long time energy conservation by high order geometric integrators
AbstractThe main aim of this paper is to investigate the long-time behavior of three high order geometric integrators, namely an…
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…
Stable spectral collocation solutions to Cauchy problems for nonlinear dispersive wave equations
AbstractIn this paper we are concerned with accurate and stable spectral collocation solutions to initial-boundary value problems attached to some challenging nonlinear…
On the numerical treatment of the eigenparameter dependent boundary conditions
AbstractIn this paper, we consider the numerical treatment of singular eigenvalue problems supplied with eigenparameter dependent boundary conditions using spectral…
Laguerre collocation solutions to boundary layer type problems
AbstractIn this paper a Laguerre collocation type method based on usual Laguerre functions is designed in order to solve high…
Pseudospectral solutions to some singular nonlinear BVPs. Applications in nonlinear mechanics
AbstractWe solve by Laguerre collocation method two second order genuinely nonlinear singularly perturbed boundary value problems and a fourth order…
Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems
AbstractIn numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that…