The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

We consider the kinetic Fokker–Planck equation with a class of general force. prove existence and uniqueness positive normalized equilibrium (in case force) establish some exponential rate convergence to (and can be explicitly computed). Our results improve about classical force case. result also improves for Fitzhugh–Nagumo from non-quantitative quantitative explicit rate.

Wave equation is one of the second order linear hyperbolic equation. Telegraph as a special case wave has interesting point to investigate in numerical view. In this paper, we consider methods for dimensional telegraph by using cubic B-spline collocation method. Collocation method solve partial differential model problem. Cubic spline interpolation an third polynomial. This polynomial interpola...

This paper investigates travelling wave solutions of the FitzHugh-Nagumo equation from the viewpoint of fast-slow dynamical systems. These solutions are homoclinic orbits of a three dimensional vector field depending upon system parameters of the FitzHugh-Nagumo model and the wave speed. Champneys et al. [A.R. Champneys, V. Kirk, E. Knobloch, B.E. Oldeman, and J. Sneyd, When Shilnikov meets Hop...

In this paper, a collocation approach is employed for the solution of the one-dimensional telegraph equation based on cubic B-spline. The derived method leads to a tri-diagonal linear system. Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory. The obtained numerical results have been compared with the results obtained b...

An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of piecewise deterministic Markov processes [9], including a broader category of random systems. The corresponding Liouville-Master Equation is established and the upwind method is applied to numerical calculation of the distribution function. The convergence of the numerical solutio...

Abstract We study some functionals associated with a process driven by fractional boundary value problem (FBVP for short). By FBVP we mean Cauchy condition written in terms of equation, that is an equation involving time-fractional derivative the sense Caputo. focus on lifetimes and additive characterizing conditions. show corresponding are related to telegraph equations. Moreover, order gives ...

We study the well-posedness of a coupled system of PDEs and ODEs arising in the numerical simulation of electrocardiograms. It consists of a system of degenerate reaction-diffusion equations, the so-called bidomain equations, governing the electrical activity of the heart, and a diffusion equation governing the potential in the surrounding tissues. Global existence of weak solutions is proved f...