High-fidelity numerical simulation of solitons in the nerve axon

Abstract

High-order accurate finite difference schemes are derived for a non-linear soliton model of nerve signal propagation in axons. Two types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP-SAT approximation is time-integrated with an explicit finite difference method. The accuracy and stability properties of the newly derived finite difference approximations are demonstrated for an analytic soliton solution.