In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

This paper contains a computational approximation for the solution of a forward-backward differential equation that models nerve conduction in a myelinated axon. We look for a solution of an equation defined in R, which tends to known values at ±∞. Extending the approach introduced in [5, 10, 6] for linear case, a numerical method for the solution of problem, is adapted to non linear case using...