High-fidelity numerical simulation of solitons in the nerve axon

Jonatan Werpers
Division of Scientific Computing
Department of Information Technology
Uppsala University


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 weakly using a penalty technique to guarantee linear stability. The resulting finite difference approximations lead to fully explicit time integration. The accuracy and stability properties of the newly derived finite difference approximations are demonstrated for a 1-D soliton solution.