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 [R.A. Van Gorder, 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.