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We construct a numerical solution of an optimal control problem for Oskolkov's equations system. The system models the dynamics of Kelvin-Voigt viscoelastic fluid. Solutions of the original boundary problem and of the conjugate problem are found numerically by means of the difference schemes method. We apply the approach of the research of evolution systems that are not solvable with respect to the time derivative. The optimization is performed using the conditional gradient method. We present the numerical experiment.

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