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An iterative approach to construction numerical methods second order based on the method of LinigurWhillaby, that have minimal error of discretization is proposed. The essence of the approach in defining amendments to the explicit and implicit Euler's method at the time when their contributions are equivalent. The stability conditions for this class of methods are obtained by the example of conservative systems. The confirmed improving of characteristics time and accuracy in the process of computation in quartz generators 9 order. Keywords— numerical methods; discretization; stability conditions, quartz generators; auto-oscillation system; discrete formula; error of discretization.

ANALYSIS OF STABILITY OF ONE CLASS OF NUMERICAL METHODS OF SECOND ORDER