Analytical and numerical solutions of the density dependent diffusion Nagumo equation

In this Letter, we obtained solutions to a class of density dependent diffusion Nagumo equations. In particular, series solutions are obtained, along with a bound for the range of the convergence. Also, numerical solutions are obtained by the Runge–Kutta–Fehlberg 45 method. Moreover, the dependence of the traveling wave solutions on various parameters is discussed. Furthermore, we compare the series solutions with the numerical solutions to validate the numerical method. The results obtained in this study reveal many interesting behaviors that warrant further study on the Nagumo equation.