A boundary function equation and its numerical solution

We consider the asymptotic solution of the plasma-sheath integro-differential equation, which is singularly perturbed due to the presence of a small coefficient multiplying the highest order (second) derivative. The asymptotic solution is obtained by the boundary function method. A second-order differential equation is derived describing the behavior of the zeroth-order boundary functions. A numerical algorithm for this equation is discussed. __________ Translated from Prikladnaya Matematika i Informatika, No. 24, pp. 24–34, 2006.