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Computational Methods for a Mathematical Model of Propagation of Nerve Impulses in Myelinated Axons

Lima, Pedro M.; Ford, Neville J.; Lumb, Patricia M.

Applied Numerical Mathematics, 85 (2014), 38-53

This paper is concerned with the approximate solution of a nonlinear mixed type functional differential equation (MTFDE) arising from nerve conduction theory. The equation considered describes conduction in a myelinated nerve axon. We search for a monotone solution of the equation defined in the whole real axis, which tends to given values at ±?. We introduce new numerical methods for the solution of the equation, analyse their performance, and present and discuss the results of the numerical simulations.