This research investigates integral problems in hyperbolic systems, revealing solvability conditions and convergence of approximate solutions.
An integral problem for hyperbolic system second order with a generalized piecewise-constant argument (GPCA) is investigated. For solution to problem, the method of introducing auxiliary functions is employed alongside Dzhumabaev parametrization method. Solvability conditions of investigated problem derived from non-singularity of a specific matrix. Additionally, an approach for computing an approximate solution is proposed, and we show that it converges to the exact solution.
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Imanchiyev et al. (2025) studied this question.
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