Related papers: An integration scheme for reaction-diffusion model…
We introduce a fully generalized quiescent chemical reactor system in arbitrary space $\vdim =1,2$ or 3, with $n\in\mathbb{N}$ chemical constituents $\alpha_{i}$, where the character of the numerical solution is strongly determined by the…
A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production…
The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian Dynamics (BD) or…
Reaction-diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to…
The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture,…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
Traditional cutoff regularization schemes of the Nambu--Jona-Lasinio model limit the applicability of the model to energy-momentum scales much below the value of the regularizing cutoff. In particular, the model cannot be used to study…
In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…
For reaction-diffusion equations in irregular domain with moving boundaries, the numerical stability constraints from the reaction and diffusion terms often require very restricted time step size, while complex geometries may lead to…
Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…
In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…
A wide range of new Q-conditional symmetries for reaction-diffusion systems with power diffusivities are constructed. The relevant non-Lie ansatze to reduce the reaction-diffusion systems to ODE systems and examples of exact solutions are…
The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…