Abstract
A boundary-value problem for a class of singularly perturbed systems of nonlinear ordinary differential equations is considered. An analytic-numerical method for solving this problem is proposed. The method combines the operational Newton method with the method of continuation by a parameter and construction of the initial approximation in an explicit form. The method is applied to the particular system arising when simulating the interaction of physical fields in a semiconductor diode. The Frechet derivative and the Green function for the corresponding differential equation are found analytically in this case. Numerical simulations demonstrate a high efficiency and superexponential rate of convergence of the method proposed.
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