V.N. Biryukov, A.M. Pilipenko, D.G. Kovtun

The main difficulty in the implementation of most standard implicit Runge-Kutta methods applied to oscillating differential equations is to efficiently solve the nonlinear system of equations. In this article we propose the estimation the accuracy of numerical methods by period and amplitude errors of sine wave, not by conventional local or global errors. The methodology is particularly useful when applied to systems with losses, since P-stability is used to linear lossless systems only. Exclusively transient analysis оf oscillators was considered irrelatively to selection of initial conditions or boundary conditions, however this technique applicable for methods of analysis in frequency domain. Received results supplement known analytical estimations of properties of numerical methods of solution of ordinary differential equations for lossless circuits. In this paper the possibility of accurate determination оf oscillator parameters asymptotic error for any numerical methods of solution of ordinary differential equations was shown for the first time.