WS

W.M. Schouten-Straatman

7 records found

Authored

We investigate the impact of spatial-temporal discretisation schemes on the dynamics of a class of reaction-diffusion equations that includes the FitzHugh-Nagumo system. For the temporal discretisation we consider the family of six backward differential formula (BDF) methods, whi ...
We show that functional differential equations of mixed type (MFDEs) with infinite range discrete and/or continuous interactions admit exponential dichotomies, building on the Fredholm theory developed by Faye and Scheel for such systems. For the half line, we refine the earlier ...
We survey some recent results on traveling waves and pattern formation in spatially discrete bistable reaction-diffusion equations. We start by recalling several classic results concerning the existence, uniqueness and stability of travelling wave solutions to the discrete Nagumo ...
We establish the existence and nonlinear stability of traveling wave solutions for a class of lattice differential equations (LDEs) that includes the discrete FitzHugh--Nagumo system with alternating scale-separated diffusion coefficients. In particular, we view such systems as s ...
We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we need to study a functional differential eq ...
If L and M are partially ordered vector spaces, then one can consider regular linear maps from L to M, i.e. linear maps which can be written as the difference of two positive linear maps. If the space L is directed, then the space Lr(L,M) of all regular linear operators becomes a ...

Contributed

We analyze the spatially discretized version of the Allen-Cahn partial differential equation. The second order derivative is numerically approximated by a weighted infinite sum. The coefficients of this sum as well as the function f in the differential equation have got freedom i ...