Analytical and numerical solutions of the density dependent Nagumo telegraph equation

In this paper, we obtained analytical and numerical solutions to a class of density dependent diffusion equations with memory-delay effect. This is a generalization of the density dependent diffusion Nagumo equation we studied recently [RA. Van Corder, K. Vajravelu, Physics Letters A 372 (2008) 5152]. Furthermore, we obtained series solutions for various strengths of the density dependence along with bounds on the range of the convergence. The numerical solutions are obtained by the Runge-Kutta-Fehlberg 45 method. The dependence of the traveling wave solutions on various parameters, particularly the memory-delay term, is discussed. (C) 2010 Elsevier Ltd. All rights reserved.