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Numerical Solutions of some Nonlinear Integral Equations Arising in the Theory of \(p\)-Adic Strings and Physical Kinetics

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Abstract

The present work is devoted to finding numerical solutions of two types of nonlinear integral equations on half line with kernels depending on the sum and difference of arguments. These equations arise in various fields of mathematical physics: kinetic theory of gases, theoretical astrophysics, p-adic string theory, etc. The main result of the work is the derivation of an uniform estimate of the norm of difference between two successive approximations of solutions, which plays an important role for the control of the convergence of iterative schemes and number of iterations. The obtained results have been applied to determine numerical solutions of models from different areas of applications.

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Acknowledgments

The authors express deep gratitude to the referee for useful remarks.

Funding

The research by the first author was conducted under the support of the Science Committee, Republic of Armenia, within research project 23RL-1A027. The research by the second author was conducted under the support of the Science Committee, Republic of Armenia, within research project 21T-1A047.

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, Yerevan State University, Alex Manoogian 1, Yerevan, 0025, Republic of Armenia

    Kh. A. Khachatryan

  2. Department of Higher Mathematics, Physics and Applied Mechanics, Armenian National Agrarian University, Teryan 74, Yerevan, 0009, Republic of Armenia

    A. Kh. Khachatryan

  3. Institute of Mathematics of NAS of Armenia, Baghramyan 24/5, Yerevan, 0019, Republic of Armenia

    A. Kh. Khachatryan

  4. Department of Mathematics and Computer Science, University of Bremen, Bibliothekstr. 1, Bremen, 28359, Germany

    A. Zh. Narimanyan

Authors
  1. Kh. A. Khachatryan
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  2. A. Kh. Khachatryan
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  3. A. Zh. Narimanyan
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Correspondence to Kh. A. Khachatryan, A. Kh. Khachatryan or A. Zh. Narimanyan.

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Khachatryan, K.A., Khachatryan, A.K. & Narimanyan, A.Z. Numerical Solutions of some Nonlinear Integral Equations Arising in the Theory of \(p\)-Adic Strings and Physical Kinetics. P-Adic Num Ultrametr Anal Appl 16, 43–59 (2024). https://doi.org/10.1134/S2070046624010047

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  • DOI: https://doi.org/10.1134/S2070046624010047

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