Asymptotic methods in mechanics of solids by Svetlana M. Bauer Sergei B. Filippov Andrei L. Smirnov Petr E. Tovstik & Rémi Vaillancourt

Author:Svetlana M. Bauer, Sergei B. Filippov, Andrei L. Smirnov, Petr E. Tovstik & Rémi Vaillancourt
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In the particular case , we have

The series (4.1.20) is also divergent.

4.1.3 Asymptotic Solutions of Parameter-Free Equations

The above algorithm for the construction of solutions may be applied to some linear equations not containing the parameter as . Consider the equation

(4.1.22)

in the domain for

(4.1.23)

After the change of variable , Eq. (4.1.22) takes the form (4.1.1) where .

As before, we seek a solution in the form (4.1.2). Since the coefficients are constant, the roots (4.1.8) of Eq. (4.1.7) are also constant. For the simple root , Eqs. (4.1.4), (4.1.5), provide the system

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