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One Approach to the Solution of a Nonlocal Problem for Systems of Hyperbolic Equations with Integral Conditions

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We consider a nonlocal problem with integral conditions for a system of hyperbolic equations with two independent variables. We study the solvability of the considered problem and construct algorithms aimed at finding its approximate solutions by introducing additional functional parameters. The investigated problem is reduced to an equivalent problem that consists of the Goursat problem for a system of hyperbolic equations with parameters and a boundary-value problem with integral condition for a system of ordinary differential equations for the introduced parameters. We propose algorithms for finding approximate solutions of the problem based on the algorithms used for the solution of the equivalent problem and prove their convergence to the exact solution.

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Simulation, Ministry of Education and Science of the Republic of Kazakhstan, Pushkin Str., 125, Almaty, 050010, Kazakhstan

    A. T. Asanova

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  1. A. T. Asanova
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Correspondence to A. T. Asanova.

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Translated from Neliniini Kolyvannya, Vol. 20, No. 4, pp. 435–450, October–December, 2017.

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Asanova, A.T. One Approach to the Solution of a Nonlocal Problem for Systems of Hyperbolic Equations with Integral Conditions. J Math Sci 238, 189–206 (2019). https://doi.org/10.1007/s10958-019-04228-7

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  • DOI: https://doi.org/10.1007/s10958-019-04228-7

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