Abstract
We introduce the standard terminology used in perturbation methods and asymptotic analysis. Asymptotic expansions will be employed to construct solutions to introductory problems in algebraic/transcendental equations and ordinary differential equations. In particular, we introduce the iteration and expansion methods for solving such equations and distinguish between regular and singular problems.
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Notes
- 1.
Trivial solutions (\(x\equiv 0\)) are exact solutions only if they satisfy the full problem for all \(\varepsilon \).
- 2.
It is a “ghost” of the \(x_B\) regular solution, which is \(O(\varepsilon )\) in terms of X (and violates requirement (i) in Sect. 6.3.2).
- 3.
Use of a computer algebra program (Maple or Mathematica) is recommended for solving many of the more algebraically intensive problems.
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© 2015 Springer International Publishing Switzerland
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Witelski, T., Bowen, M. (2015). Perturbation Methods. In: Methods of Mathematical Modelling. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23042-9_6
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DOI: https://doi.org/10.1007/978-3-319-23042-9_6
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-23042-9
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