Editing Runge–Kutta methods (section)

{{Short description|Family of implicit and explicit iterative methods}}
[[File:Comparison of the Runge-Kutta methods for the differential equation (red is the exact solution).svg|thumb|upright=1.25|Comparison of the Runge-Kutta methods for the differential equation <math>y'=\sin(t)^2 \cdot y</math> (red is the exact solution)]]
{{Differential equations}}

In [[numerical analysis]], the '''Runge–Kutta methods''' ({{IPAc-en|lang|ˈ|r|ʊ|ŋ|ə|ˈ|k|ʊ|t|ɑː|audio=en-us-Runge-Kutta.ogg}} {{Respell|RUUNG|ə|KUUT|tah}}<ref>{{cite web |title=Runge-Kutta method |url=https://www.dictionary.com/browse/runge-kutta-method |website=[[Dictionary.com]] |access-date=4 April 2021 |language=en}}</ref>) are a family of [[Explicit and implicit methods|implicit and explicit]] iterative methods, which include the [[Euler method]], used in [[temporal discretization]] for the approximate solutions of [[simultaneous nonlinear equations]].<ref>DEVRIES, Paul L.; HASBUN, Javier E. A first course in computational physics. Second edition. Jones and Bartlett Publishers: 2011. p. 215.</ref> These methods were developed around 1900 by the German mathematicians [[Carl Runge]] and [[Wilhelm Kutta]].