Parametrically defined differential equations

[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.

[发布机构] 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

[效力级别] 数学

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