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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
Article
  • 28 Downloads

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 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.

Keywords

Green Function Initial Approximation Transmission Condition Integral Identity Principal Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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