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…
Posts by Călin-Ioan Gheorghiu
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…
Analytical and numerical solutions to an electrohydrodynamic stability problem
AbstractA linear hydrodynamic stability problem corresponding to an electrohydrodynamic convection between two parallel walls is considered. The problem is an…
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…
Publications
Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media
AbstractFlow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number of…
Read More Functional differential equations with maxima, via step by step contraction principle
AbstractT. A. Burton presented in some examples of integral equations a notion of progressive contractions on C([a, ∞[). In 2019, I. A. Rus formalized this notion (I. A. Rus, Some…
Read More How many steps still left to x*?
Emil Cătinaş
(original), (survey), Convergence orders, Fixed point theory, history, ISI/JCR, iterative methods, local convergence, Newton method, nonlinear equations in R, Numerical Analysis, paper, secant/chord method, successive approximations
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Abstract The high speed of \(x_{k}\rightarrow x^\ast\in{\mathbb R}\) is usually measured using the C-, Q- or R-orders: \begin{equation}\tag{$C$} \lim \frac {|x^\ast – x_{k+1}|}{|x^\ast – x_k|^{p_0}}\in(0,+\infty), \end{equation} \begin{equation}\tag{$Q$} \lim \frac {\ln…
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