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Approximate Analytical Methods for Solving Ordinary Differential Equations, 2015, p.114-139
Ort / Verlag
United Kingdom: Chapman and Hall/CRC
Erscheinungsjahr
2015
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
In this chapter, we introduce another asymptotic method for solving singularly perturbed problems called the WKB approximation,
named after the physicists Gregor Wentzel, Hendrik Kramers, and
Léon Brillown, who all developed it in 1926. This approximation
is considered to be the most powerful tool for obtaining global
approximations to the solutions of singularly perturbed equations
but is applicable only to linear differential equations. Although
this method was developed basically for solving singularly perturbed problems, it can be used to solve unperturbed problems as
well. Note also that the problems involving large parameters and
the problems for which we have to find solutions at irregular singular points (IRSPs) also can be solved easily using this method (see
Example 6.1 of this chapter). In addition, problems with rapidly
oscillating solutions can be solved using this method (Bender and
Orszag, 1999).