Numerical Approximation of a Nonlinear Boundary Value Problem for a Mixed Type Functional Differential Equation Arising in Nerve Conduction

Abstract

This paper is concerned with the approximate solution of a nonlinear mixed type functional differential equation (MTFDE) with deviating arguments arising from nerve conduction theory. The considered equation describes conduction in a myelinated nerve axon in which the myelin totally insulates the membrane. As a consequence, the potential change jumps from node to node. As described in [2], this process is modelled by a first order nonlinear functional‐differential equation with deviated arguments. We search for a solution of this equation defined in R, which tends to given values at ±∞. Following the approach introduced in [13] and [8], we propose and analyze some new computational methods for the solution of this problem. Numerical results are obtained and compared with the ones presented in [2].