Related papers: Comments on the paper "Solutions of Multitime Reac…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of…
This paper is concerned with reaction-diffusion-advection equations in spatially periodic media. Under an assumption of weak stability of the constant states 0 and 1, and of existence of pulsating traveling fronts connecting them, we show…
We comment on a recent article published in Phys. Rev. D98 (2018) no.9, 094513, arXiv:1811.09029, pointing out severe problems in the numerical investigation leading to questionable results and misleading conclusions during their…
A class of coupled time-space fractional reaction-diffusion systems derived from reversible chemical reactions over a bounded domain is investigated. Employing mainly an appropriate Lyapunov functional and an improved maximum principle, we…
If accepted, the paper will be available at http://pubs.acs.org/journals/jpcbfh/
In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for…
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…
Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy…
The stochastic solution to diffusion equations with polynomial coefficients is called a Pearson diffusion. If the time derivative is replaced by a distributed fractional derivative, the stochastic solution is called a fractional Pearson…
This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best…
We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
Comments are made on some recently published papers on matter collineations of plane symmetric, cylindrically symmetric and spherically symmetric spacetimes.
In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with $m\geq 2$ population densities. We introduce a discrete multi-phase…
A symmetry group classification for fourth-order reaction-diffusion equations, allowing for both second-order and fourth-order diffusion terms, is carried out. The fourth order equations are treated, firstly, as systems of second-order…
The title paper is discussed critically. There are major problems with incorrect statements, irrelevant citations, incorrect mathematics leading to incorrect results, which are compared with our own simulations.