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Progress in developing Poisson-Boltzmann equation solvers

Chuan Li, Lin Li, Marharyta Petukh, Emil Alexov (2013)

Molecular Based Mathematical Biology

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided...

Projection method with level control in convex minimization

Robert Dylewski (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study a projection method with level control for nonsmoooth convex minimization problems. We introduce a changeable level parameter to level control. The level estimates the minimal value of the objective function and is updated in each iteration. We analyse the convergence and estimate the efficiency of this method.

Propagation of chaos for the 2D viscous vortex model

Nicolas Fournier, Maxime Hauray, Stéphane Mischler (2014)

Journal of the European Mathematical Society

We consider a stochastic system of N particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...

Propagation of errors in dynamic iterative schemes

Zubik-Kowal, Barbara (2017)

Proceedings of Equadiff 14

We consider iterative schemes applied to systems of linear ordinary differential equations and investigate their convergence in terms of magnitudes of the coefficients given in the systems. We address the question of whether the reordering of equations in a given system improves the convergence of an iterative scheme.

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