In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where spatial adaptivity geometrical singularities and boundary layer effects are mainly considered. As a key contribution, equations studied systematically rigorous analysis residual-based posteriori error estimate of system is presented. With regularity linearized derive...

Abstract Electrolyte-gated organic field-effect transistors (EGOFETs) represent a class of thin-film suited for sensing and biosensing in aqueous media, often at physiological conditions. The EGOFET device includes electrodes an semiconductor channel direct contact with electrolyte. Upon operation, electric double layers are formed along the gate-electrolyte channel-electrolyte interfaces, but ...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) equations, which has found much use in diverse applications. Our DG method with Euler forward time discretization is shown to preserve positivity cell averages at all steps. The numerical solutions then restored by a sc...

In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one variable, several variables, methods of solution and its applications, especially dealing with laser statistics. There has been a considerable progress on the topic as well as the topic has received greater...

Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, ...