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Analysis and computational approximation of a forward-backward equation arising in nerve conduction

Lima, Pedro M.; Teodoro, Filomena; Ford, N. J.; Lumb, P. M.

Differential and Difference Equations with Applications, Springer Proceedings in Mathematics & Statistics, Springer, New York, 47 (2013), 475-483

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 solution defined on the whole real axis, which tends to given values at ±?.The numerical algorithms, developed previously by the authors for linear problems, were upgraded to deal with the case of nonlinear problems on unbounded domains. Numerical results are presented and discussed.