Journal of Mathematical Sciences

, Volume 149, Issue 4, pp 1385–1399 | Cite as

Effective method for solving singularly perturbed systems of nonlinear differential equations

  • S. I. Bezrodnykh
  • V. I. Vlasov


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.


Green Function Initial Approximation Transmission Condition Integral Identity Principal Term 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Computational Center of RASMoscow

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