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…
Numerical Analysis
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…
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…
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…
Spectral collocation solutions to multiparameter Mathieu’s system
AbstractOur main aim is the accurate computation of a large number of specified eigenvalues and eigenvectors of Mathieu’s system as…
Stable spectral collocation solutions to a class of Benjamin Bona Mahony initial value problem
AbstractWe are concerned with stable spectral collocation solutions to non-periodic Benjamin Bona Mahony (BBM), modified BBM and Benjamin Bona Mahony-Burgers…