Geodesic
Effective method for solving singularly perturbed systems of nonlinear differential equations
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 45-58 
S. I. Bezrodnykh; V. I. Vlasov. Effective method for solving singularly perturbed systems of nonlinear differential equations. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 45-58. http://geodesic.mathdoc.fr/item/CMFD_2006_15_a4/
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     author = {S. I. Bezrodnykh and V. I. Vlasov},
     title = {Effective method for solving singularly perturbed systems of nonlinear differential equations},
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     year = {2006},
     volume = {15},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_15_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 Frechét 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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