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Iteration Method for Solving a Nonlinear Boundary Value Problem with a Point Source

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Abstract

 In this paper, we consider the first boundary value problem for a quasilinear equation in a bounded domain with a point source. The solution of the problem is sought as the sum of three functions. The first function is represented explicitly and is the solution of a linear constant coefficient equation with a point source. The second function can be found from the solution of a linear homogeneous boundary value problem with constant coefficients. To find the third function, an iterative process is used that converges strongly at the rate of a geometric progression in a Sobolev space.

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REFERENCES

  1. O. A. Zadvornov, “Existence of solutions for quasilinear elliptic boundary value problem in the presence of point sources,” Uch. Zap. Kazan. Gos. Univ. Fiz.-Mat. Nauki 152 (1), 155–163 (2010).

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Funding

This work was supported by the Kazan Federal University Strategic Academic Leadership Program (“PRIORITY-2030”).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Information Technologies, Kazan Federal University, 420008, Kazan, Russia

    O. A. Zadvornov & G. O. Trifonova

Authors
  1. O. A. Zadvornov
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  2. G. O. Trifonova
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Corresponding authors

Correspondence to O. A. Zadvornov or G. O. Trifonova.

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The authors declare that they have no conflicts of interest.

Additional information

Translated by I. Tselishcheva

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Zadvornov, O.A., Trifonova, G.O. Iteration Method for Solving a Nonlinear Boundary Value Problem with a Point Source. Russ Math. 66, 60–64 (2022). https://doi.org/10.3103/S1066369X22050085

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  • DOI: https://doi.org/10.3103/S1066369X22050085

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