Fourth-order Runge–Kutta method

GPTKB entity

Predicate	Object
gptkbp:instanceOf	Numerical method Ordinary differential equation solver
gptkbp:accuracy	Fourth-order
gptkbp:advantage	Good balance of accuracy and computational cost Not suitable for stiff equations
gptkbp:alsoKnownAs	gptkb:RK4
gptkbp:application	Chemical kinetics Physics simulations Biological modeling Engineering problems
gptkbp:appliesTo	Ordinary differential equations
gptkbp:category	gptkb:Explicit_Runge–Kutta_methods
gptkbp:commonIn	gptkb:Control_theory gptkb:Computational_biology Numerical analysis Computational physics Scientific computing
gptkbp:developedBy	gptkb:Carl_Runge gptkb:Wilhelm_Kutta
gptkbp:firstSlope	k1
gptkbp:form	Weighted average of slopes
gptkbp:fourthSlope	k4
gptkbp:globalErrorOrder	O(h^4)
https://www.w3.org/2000/01/rdf-schema#label	Fourth-order Runge–Kutta method
gptkbp:implementedIn	gptkb:Java gptkb:Python gptkb:Fortran gptkb:Julia gptkb:C++ gptkb:MATLAB gptkb:Mathematica gptkb:Octave R
gptkbp:introducedIn	1901
gptkbp:localErrorOrder	O(h^5)
gptkbp:numberOfFunctionEvaluationsPerStep	4
gptkbp:order	4
gptkbp:relatedTo	gptkb:Runge–Kutta_methods gptkb:Heun's_method gptkb:Euler_method
gptkbp:requires	Function evaluations
gptkbp:secondSlope	k2
gptkbp:stable	Conditionally stable
gptkbp:step	h Single-step method
gptkbp:thirdSlope	k3
gptkbp:updateFormula	y_{n+1} = y_n + (1/6)(k1 + 2k2 + 2k3 + k4)
gptkbp:usedFor	Solving initial value problems
gptkbp:bfsParent	gptkb:Runge–Kutta_methods
gptkbp:bfsLayer	6