Related papers: Numerical Solutions of Reaction-Diffusion Equation…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…
We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…
In this comprehensive and detailed study, vacancy-mediated self-diffusion of A- and B-elements in 'triple-defect' B2-ordered ASB(1-S) binaries is simulated by means of a kinetic Monte Carlo (KMC) algorithm involving atomic jumps to…
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
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…
In this article, we carry out a study of long-term behavior of reaction-diffusion systems augmented with self- and cross-diffusion, using an augmented Gray-Scott system as a general example. The methodology remains generic, and is therefore…
In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, $\partial_t u + a \cdot \nabla u = \Delta u + F (x, t, u)$, $x \in \Omega \subset \mathbf{R}^3$, $t > 0$. Here, $u$ is a…
In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a…
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples\ related to pure advection in a finitely long channel and the distribution of an initial…
We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…
An operator-splitting finite element scheme for the time-dependent, high-dimensional radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite…
We use the perturbation method to approximately solve subdiffusion-reaction equations. Within this method we obtain the solutions of the zeroth and the first order. The comparison our analytical solutions with the numerical results shown…
This paper implements an efficient numerical algorithm for the time-fractional Black-Scholes model governing European options. The proposed method comprises the Crank-Nicolson approach to discretize the time variable and exponential…
Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…
We study an autocatalytic reaction-diffusion scheme, the Gray-Scott model, when the mixing processes do not homogenize the reactants. Starting from the master equation, we derive the resulting coupled, nonlinear, stochastic partial…