Abstract
The method of freezing proposed and given a foundation by A.N. Filatov, for systems of integrodifferential equations (IDE) of standard form /1–4/ is applied to IDE systems encountered in dynamic viscoelasticity problems. A numerical method is proposed for IDE systems, which is based on using quadrature formulas. A specific example is examined to compare this method with other known methods (the method of averaging and the method of freezing). Furthermore, a problem on the longitudinal vibrations of a viscoelastic rod in a physically non-linear formulation is investigated by the method of freezing in combination with a numerical Runge-Kutta method.
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