Ergodic simulations of diffusion in random velocity fields
AbstractErgodic simulations aim at estimating ensemble average characteristics of diffusion in random fields from space averages. The traditional approach, based…
book chapter
Global random walk algorithm for diffusion processes
AbstractThe Global Random Walk algorithm (GRW) performs the simultaneous tracking on a fixed grid of large collections of particles, while…
Ergodic Estimations of Upscaled Coefficients for Diffusion in Random Velocity Fields
AbstractUpscaled coefficients for diffusion in ergodic velocity fields are derived by summing up correlations of increments of the position process,…
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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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