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SOURCE:    Almanac of Modern Science and Education. Tambov: Gramota, 2016. № 2. P. 106-115.
SCIENTIFIC AREA:    Physical-Mathematical Sciences
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DEPENDENCE OF SOLUTIONS OF THE SECOND-ORDER DIFFERENTIAL EQUATION ON THE SMALL PARAMETER AT THE HIGHEST DERIVATIVE
Pyrkova Ol'ga Anatol'evna
Moscow Institute of Physics and Technology (State University)
Abstract. This article discusses two ways of the solution of the boundary value problem for the ordinary second-order linear differential equation with the small parameter at the highest derivative. The first one is based on the theorem on the reduction of the boundary value problem in this case to Cauchy problem for the first-order equation, the proof of which forestalls the solution. The second one uses the direct solution of the boundary value problem followed by the expansion of the solution by Taylor’s formula.
Key words and phrases: дифференциальные уравнения, краевая задача, задача Коши, малый параметр, пограничный слой, формула Тейлора, differential equations, boundary value problem, Cauchy problem, small parameter, boundary layer, Taylor’s formula
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References:
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  2. Diesperov V. N. Differentsial'nye i raznostnye uravneniya: uchebno-metodicheskoe posobie. M.: Fiztekh-Poligraf, 2007. 58 s.
  3. Pyrkova O. A. Sposob resheniya matematicheskoi zadachi v zavisimosti ot tselei obucheniya // XXIII Mezhdunarodnaya konferentsiya. Matematika. Komp'yuter. Obrazovanie. Biofizika slozhnykh sistem. Molekulyarnoe modelirovanie. Sistemnaya biologiya: simpozium s mezhdunarodnym uchastiem: tezisy. V. 23 / pod red. G. Yu. Riznichenko i A. B. Rubina. M. - Izhevsk, 2016.
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