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Kondakova Svitlana

National Aviation University


SOLUTION THE SYSTEMES  OF LINEAR DIFFERENTIAL EQUATIONS BY THE METHOD OF  THE INDIGNANT
CHARACTERISTIC  EQUATION.

 Consider the system of the linear differential equations

$$\varepsilon ^ hW (t) \frac {dy} {dt} = C (t, \varepsilon) y. $$ If the characteristic
equation
 $$\det \ | C _ 0 (t) -\lambda W (t) \ | = 0 $$
 has a multiple root, to which correspondeet the simple elementary dividers, at $ h = 1 $
 М. Shkil has shown, that initial system can be to reduce to the differential system, which
 is integrated by a method of consecutive approximations. At $ h> 1 $, received by analogy,
 the decision in regular intervals will not converge to exact.

 The method of the indignant characteristic equation allows to reduce this case to a case
 various characteristic numbers. The received decision at certain additional
 conditions will satisfy initial system to within size of the order of $O(\varepsilon^{2h-1})$.
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