Parametrically defined differential equations

5th International Conference on "Problems of Mathematical and Theoretical Physics and Mathematical Modelling"

物理学;数学

Polyanin, A.D.^1,2,3 ; Zhurov, A.I.^1,4

Institute for Problems in Mechanics, Russian Academy of Sciences, 101 Vernadsky Avenue, bldg 1, Moscow

119526, Russia^1

Bauman Moscow State Technical University, 5 Second Baumanskaya Street, Moscow

105005, Russia^2

National Research Nuclear University MEPhI, 31 Kashirskoe Shosse, Moscow

115409, Russia^3

Cardiff University, Heath Park, Cardiff

CF14 4XY, United Kingdom^4

关键词: Arbitrary functions;    Cauchy problems;    Exact solution;    General solutions;    Nonlinear differential equation;    Nonlinear ordinary differential equation;    Numerical solution;    Standard system;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012028/pdf
DOI  :  10.1088/1742-6596/788/1/012028

来源: IOP

【 摘 要 】

The paper deals with nonlinear ordinary differential equations defined parametrically by two relations. It proposes techniques to reduce such equations, of the first or second order, to standard systems of ordinary differential equations. It obtains the general solution to some classes of nonlinear parametrically defined ODEs dependent on arbitrary functions. It outlines procedures for the numerical solution of the Cauchy problem for parametrically defined differential equations.