Analytical and numerical solutions of the density dependent diffusion Nagumo equation

DOI10.1016/j.physleta.2008.05.068zbMath1221.92026OpenAlexW2035175601MaRDI QIDQ717063

Robert A. van Gorder, Kuppalapalle Vajravelu

Publication date: 27 September 2011

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2008.05.068

zbMATH Keywords

Runge-Kutta-Fehlberg 45 method

Mathematics Subject Classification ID

Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Traveling wave solutions (35C07)

Related Items (9)

A geometric approach for solving the density-dependent diffusion Nagumo equation ⋮ Numerical simulation of thin paint film flow ⋮ Gaussian waves in the Fitzhugh-Nagumo equation demonstrate one role of the auxiliary function \(H(x, t)\) in the homotopy analysis method ⋮ Pseudospectral methods for Nagumo equation ⋮ Reductions and new exact solutions of the density-dependent Nagumo and Fisher equations ⋮ Analytical and numerical solutions of the density dependent Nagumo telegraph equation ⋮ Painlevé test, integrability, and exact solutions for density-dependent reaction-diffusion equations with polynomial reaction functions ⋮ A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation ⋮ Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions

Cites Work

• Accurate computation of traveling wave solutions of some nonlinear diffusion equations
• Wave speeds of density dependent Nagumo diffusion equations, inspired by oscillating gap-junction conductance in the islets of Langerhans

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