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Published in:
2021 | OriginalPaper | Chapter
2. Mathematical Fundamentals
Authors : Wanchun Chen, Hao Zhou, Wenbin Yu, Liang Yang
Published in: Steady Glide Dynamics and Guidance of Hypersonic Vehicle
Publisher: Springer Singapore
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Abstract
Regular perturbation method (i.e. direct expansion method) is a technique used for solving the asymptotic power series of solutions to regular perturbation problems. By assuming that the solutions are in the form of power series with respect to the basis function and substituting the power series into the regular perturbation equation, we can obtain the regular equation of the problem. Then collect coefficients of like powers of \( \varepsilon \). Since the system is an identity for \( \varepsilon \), each coefficient of \( \varepsilon \) vanishes independently. Thus by setting these coefficients to zero, we can get a set of equations about the coefficients. After solving the coefficients, we can obtain the asymptotic power series of the solutions [1, 2].