Abstract
For a quadratic equation containing a small parameter regularly, and for the Duffing equation with small nonlinearity, their asymptotic solutions are constructed in the form of asymptotic Poincare series for a small parameter. The properties of the obtained asymptotic solutions when a small parameter tends to zero are analyzed. The sense of the theorem on the continuous dependence of the solution on the parameter for systems with regular perturbation is demonstrated. A Taylor series for the exact solution of the quadratic equation with small parameter is compared with its obtained asymptotic expansion. For the Duffing equation with small nonlinearity, we compare the graphs of the exact and asymptotic solutions under the same initial conditions.
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Schedule a callMore From: BULLETIN TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV. Mathematics. Mechanics
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