Initial boundary-value problems with moving boundaries for linear and nonlinear hyperbolic type equations are investigated. They model longitudinal and transverse-longitudinal oscillations of elastic cable of a variable length. Formulations of the problem considered go back to the papers by A.J. Ishlinsky [1], G.N. Savin and O.A. Goroshko [2], A.I. Vesnitsky [3]. Asymptotic and numerical methods are developed. Asymptotic integration is carried out when the small parameter is equal to the relation of velocities of the cable length variation and wave propagation. Numerical integration is done using the modified finite-difference and Runge-Kutta methods. Comparison of asymptotic and numerical solutions is carried out.
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