Runge-Kutta method of order 4

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:logic ordinary differential equation solver
gptkbp:accuracy	fourth-order
gptkbp:advantage	fixed step size not suitable for stiff equations good balance between accuracy and computational cost
gptkbp:alsoKnownAs	gptkb:RK4
gptkbp:application	biology chemistry computer science engineering finance physics
gptkbp:category	gptkb:explicit_Runge-Kutta_method
gptkbp:developedBy	gptkb:Carl_Runge gptkb:Martin_Kutta
gptkbp:firstPublished	1901
https://www.w3.org/2000/01/rdf-schema#label	Runge-Kutta method of order 4
gptkbp:k1Formula	k1 = h f(x_n, y_n)
gptkbp:k2Formula	k2 = h f(x_n + h/2, y_n + k1/2)
gptkbp:k3Formula	k3 = h f(x_n + h/2, y_n + k2/2)
gptkbp:k4Formula	k4 = h f(x_n + h, y_n + k3)
gptkbp:notableFeature	widely used in practice
gptkbp:numberOfFunctionEvaluationsPerStep	4
gptkbp:order	4
gptkbp:relatedTo	gptkb:Heun's_method gptkb:Euler_method gptkb:Dormand-Prince_method
gptkbp:requires	function evaluation step size selection
gptkbp:stable	conditionally stable
gptkbp:stepFormula	y_{n+1} = y_n + (1/6)(k1 + 2k2 + 2k3 + k4)
gptkbp:type	single-step method
gptkbp:usedFor	solving initial value problems
gptkbp:bfsParent	gptkb:RK4
gptkbp:bfsLayer	8