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Boundary-layer averaging for standard systems with lag

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Abstract

Thekth-order asymptotic solution of a standard system with lag is constructed along trajectories calculated according to the averaging scheme of A. N. Filatov. If the perturbation parameter ε ≪ 1, then the use of the step method for finding the solution is connected with cumbersome calculations because the number of required steps is inversely proportional to ε. We suggest another approach in which the step method is used onlyk times fortε [0,k] and justify the asymptotic method.

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References

  1. A. N. Filatov,Asymptotic Methods in the Theory of Differential and Integro-Differential Equations [in Russian], Fan, Tashkent (1974).

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  2. V. P. Zheltikovand and V. V. Éfendiev,Asymptotic Averaging of Standard Systems with Lag [in Russian], Deposited in the Ukr. Inst. of Sci. Eng. Inform., No. 28-Uk92, Odessa (1991).

  3. V. P. Zheltikovand and V. V. Éfendiev,Averaged Problems for Standard Systems with Lag [in Russian], Deposited in Ukr. Inst. of Sci. Eng. Inform. No. 1328-Uk92, Odessa (1992).

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  5. A. B. Vasil'eva and V. F. Butuzov,Asymptotic Methods in the Theory of Singular Perturbations [in Russian], Vysshaya Shkola, Moscow (1990).

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Authors and Affiliations

  1. Odessa University, Odessa

    V. P. Zheltikov & V. V. Éfendiev

Authors
  1. V. P. Zheltikov
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  2. V. V. Éfendiev
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10 pp. 1362–1368, October, 1994.

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Zheltikov, V.P., Éfendiev, V.V. Boundary-layer averaging for standard systems with lag. Ukr Math J 46, 1504–1511 (1994). https://doi.org/10.1007/BF01066093

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  • DOI: https://doi.org/10.1007/BF01066093

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