A fully discrete Lagrangian scheme for numerical solution of the nonlinear fourth-order
DLSS equation in one space dimension is analyzed. The discretization is based on the …

We consider the numerical solution of coupled volume-surface reaction-diffusion systems
having a detailed balance equilibrium. Based on the conservation of mass, an appropriate …

We consider a non-standard finite-volume discretization of a strongly non-linear fourth order
diffusion equation on the d-dimensional cube, for arbitrary $ d\geqslant 1$. The scheme …

Semi-discrete Runge-Kutta schemes for nonlinear diffusion equations of parabolic type are
analyzed. Conditions are determined under which the schemes dissipate the discrete …

We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the
circle. Our choice of discretization is motivated by a novel gradient flow formulation with …

New one‐leg multistep time discretizations of nonlinear evolution equations are
investigated. The main features of the scheme are the preservation of the non‐negativity and …

In this paper, we deal with two logarithmic fourth order differential equations: the extended
one-dimensional DLSS equation and its multi-dimensional analog. We show the global …

This paper presents an a priori error analysis of a fully discrete scheme for the numerical
solution of the transient, nonlinear Darcy–Nernst–Planck–Poisson system. The scheme uses …

In this paper we construct a unique global in time weak nonnegative solution to the
corrected Derrida-Lebowitz-Speer-Spohn equation, which statistically describes the …

We propose a new fully‐discretized finite difference scheme for a quantum diffusion
equation, in both one and two dimensions. This is the first fully‐discretized scheme with …