Abstract
The main aim of investigations undertaken during the early stages of research into differential equations was the derivation of exact solutions. It was subsequently found, however, that the effective representation of the exact solution in terms of elementary functions is possible only for a limited number of special classes of differential equations. Therefore, the question of methods for the construction of approximate solutions of differential equations was recognized to be the main area of research. Work in this area proceeded along two directions: a) the development of numerical methods of solution and b) the development of the so-called asymptotic methods of solution. The aim of this review is to describe asymptotic methods at their present level of development.
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Butuzov, V.F., Vasil’eva, A.B., Fedoryuk, M.V. (1970). Asymptotic Methods in the Theory of Ordinary Differential Equations. In: Gamkrelidze, R.V. (eds) Mathematical Analysis. Progress in Mathematics, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3303-6_1
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