What is Ordinary differential equation?
[[Image:Parabolic trajectory.svg|right|thumb|250px|The [[trajectory]] of a [[projectile]] launched from a [[cannon]] follows a curve determined by an ordinary differential equation that is derived from [[Newton's laws of motion|Newton's second law]].]] An '''ordinary differential equation''' (often shortened to '''ODE''') is a [[differential equation]] which contains one free variable, and its [[derivative (mathematics)|derivatives]]. Ordinary differential equations are used for many [[science|scientific]] [[model]]s and predictions. The term ''ordinary'' is used to differentiate them from [[partial differential equation]]s, which contain more than one free variable, and their derivatives. ==Numerical methods== {{main|Numerical methods for ordinary differential equations}} Since ODEs have appeared in mathematics and physics, many scientists have studied methods to solve them. But unfortunately, no one could establish methods to solve any kind of ODE. Therefore, numerical methods for ODEs are widely studied since the appearance of [[computer]]s.<ref>Mitsui, T., & Shinohara, Y. (1995). Numerical analysis of ordinary differential equations and its applications. World Scientific.</ref><ref>Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard, Solving ordinary differential equations I-II: Berlin, New York: Springer-Verlag.</ref><ref>Butcher, John C. (2008), Numerical Methods for Ordinary Differential Equations, New York: John Wiley & Sons.</ref><ref>[[Peter Deuflhard|Deuflhard, P.]], & Bornemann, F. (2012). Scientific computing with ordinary differential equations. Springer Science & Business Media.</ref><ref>Shampine, L. F. (2018). Numerical solution of ordinary differential equations. Routledge.</ref> ==Literature== * [[Vladimir Arnold|Arnolʹd, V. I.]], Ordinary differential equations. Springer. * Wolfgang Walter, Ordinary differential equations. Springer. * Logemann, H., & Ryan, E. P. (2014). Ordinary differential equations: Analysis, qualitative theory and control. Springer. * Hermann, M., & Saravi, M. (2014). A