Parametrically defined nonlinear differential equations and their solutions: Applications in fluid dynamics

被引：9

作者：

Polyanin, Andrei D. ^{[1
,2
,3
]}

Zhurov, Alexei I. ^{[1
,4
]}

机构：

[1] Russian Acad Sci, Inst Problems Mech, 101 Vernadsky Ave,Bldg 1, Moscow 119526, Russia

[2] Bauman Moscow State Tech Univ, 5 Second Baumanskaya St, Moscow 105005, Russia

[3] Natl Res Nucl Univ MEPhI, 31 Kashirskoe Shosse, Moscow 115409, Russia

[4] Cardiff Univ, Heath Pk, Cardiff CF14 4XY, Wales

来源：

APPLIED MATHEMATICS LETTERS | 2016年 / 55卷

关键词：

Parametrically defined differential equations; Nonlinear differential equations; Unsteady axisymmetric boundary layer; General solutions; Exact solutions; BOUNDARY-LAYER EQUATIONS; ORDER REDUCTION; SIMILARITY SOLUTIONS; TRANSFORMATIONS; FLOW;

D O I：

10.1016/j.aml.2015.12.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The study deals with parametrically defined ordinary differential equations, practically unaddressed in the literature. It finds the general solutions for three classes of first- and second-order nonlinear ODEs of this kind. The solutions are further used to construct new exact solutions to the equations of an unsteady axisymmetric boundary layer with pressure gradient on a body of revolution of arbitrary shape. Also the paper suggests a short list of essential problems for nonlinear ODEs and PDEs defined parametrically that need to be addressed in the future. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：72 / 80

页数：9

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