Two-timing methods with applications to heterogeneous reaction-diffusion systems

Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems

This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction–diffusion systems without monotonicity, which concludes two-species diffusion–competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non-quasimonotonicity condition. B...

Numerical Methods for Stiff Reaction-diffusion Systems

In a previous study [21], a class of efficient semi-implicit schemes was developed for stiff reaction-diffusion systems. This method which treats linear diffusion terms exactly and nonlinear reaction terms implicitly has excellent stability properties, and its second-order version, with a name IIF2, is linearly unconditionally stable. In this paper, we present another linearly unconditionally s...

Robust numerical methods for taxis-diffusion-reaction systems: Applications to biomedical problems

In this paper we consider the numerical solution of taxis–diffusion–reaction models. Such nonlinear partial differential equation models appear often in mathematical biology and we consider examples from tumour growth and invasion, and the aggregation of amoebae. These examples are characterised by a taxis term which is large in magnitude compared with the diffusion term and this can cause nume...

Reaction-Diffusion equations with applications

Discretization Methods with Analytical Characteristic Methods for Advection-diffusion-reaction Equations and 2d Applications

Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convectiondiffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerica...