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Application of the dual operator method to an equation describing the behavior of a boundary function

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Abstract

The dual operator is an analogue of the conjugate operator in linear theory. In this study the dual operator is applied to a second-order differential equation describing the behavior of the zero-order boundary function in the boundary function method used to derive the asymptotic solution of the singularly perturbed integro-differential plasma-sheath equation. This approach produces is a three-point difference scheme. The results of a numerical solution of the Cauchy problem are reported.

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References

  1. G. A. Emmert, R. M. Wieland, A. T. Mense, and J. N. Davidson, “Electric sheath and presheath in a collisionless, finite ion temperature plasma,” Phys. Fluids, 23, No. 4, 803–812 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  2. D. S. Filippychev, “Boundary function method for asymptotic solution of the plasma-sheath equation,” Prikl. Mat. Informatika, No. 19, 21–40 (2004).

    Google Scholar 

  3. A. B. Vasil’eva and V. F. Butuzov, Asymptotic Expansions of Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  4. A. B. Vasil’eva and V. F. Butuzov, Singularly Perturbed Equations in Critical Cases [in Russian], Izd. MGU, Moscow (1978).

    Google Scholar 

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

    Google Scholar 

  6. D. S. Filippychev, “Numerical solution of the differential equation describing the behavior of the zero-order boundary function,” Prikl. Mat. Informatika, No. 23, 24–35 (2006).

  7. D. G. Cacuci, R. B. Perez, and V. Protopopescu, “Duals and propagators, A canonical formalism for nonlinear equations,” J. Math. Phys., 29, No. 2, 335–361 (1988).

    Article  MathSciNet  Google Scholar 

  8. D. G. Cacuci and O. A. Karakashian, “Benchmarking the propagator method for nonlinear systems: A Burgers-Korteweg-de Vries equation,” J. Comput. Phys., 89, No. 1, 63–79 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  9. D. S. Filippychev, “Application of the dual operator formalism to obtain the zero-order boundary function for the plasma-sheath equation,” Prikl. Matem. Informatika, No. 22, 76–90 (2005).

  10. D. S. Filippychev, “Numerical solution of the differential equation for a boundary function,” Vestnik MGU, Ser. 15, Vychisl. Matem. Kibern., No. 1, 10–14 (2006).

  11. D. S. Filippychev, “Simulation of the plasma-sheath equation on a condensing grid,” Prikl. Matem. Informatika, No. 13, 35–54 (2003).

  12. D. S. Filippychev, “Simulation of the plasma-sheath equation,” Vestnik MGU, Ser. 15, Vychisl. Matem. Kibernetika, No. 4, 32–39 (2004).

  13. D. S. Filippychev, “Boundary-function equation and its numerical solution,” Prikl. Matem. Informatika, No. 24, 24–34 (2007).

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    D. S. Filippychev

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  1. D. S. Filippychev
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Correspondence to D. S. Filippychev.

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Translated from Prikladnaya Matematika i Informatika, No. 26, pp. 49–60, 2007.

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Filippychev, D.S. Application of the dual operator method to an equation describing the behavior of a boundary function. Comput Math Model 19, 271–281 (2008). https://doi.org/10.1007/s10598-008-9003-0

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