classical fourth-order Runge–Kutta method

E300768
Runge–Kutta method explicit Runge–Kutta method numerical integration method for ordinary differential equations single-step method

The classical fourth-order Runge–Kutta method is a widely used, higher-accuracy numerical technique for solving ordinary differential equations by combining multiple intermediate slope evaluations within each integration step.

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All labels observed (2)

Label Occurrences
classical fourth-order Runge–Kutta method canonical 2
RK4 1

Statements (49)

Predicate Object
instanceOf Runge–Kutta method ⓘ
explicit Runge–Kutta method ⓘ
numerical integration method for ordinary differential equations ⓘ
single-step method ⓘ
appliesToEquationForm y' = f(t, y) ⓘ
approximatesSolution sequence of values y_n at discrete times t_n ⓘ
belongsToFamily Runge–Kutta methods developed by Carl Runge and Martin Kutta ⓘ
canBeEmbeddedIn adaptive step-size Runge–Kutta pairs ⓘ
definesK1As k1 = f(t_n, y_n) ⓘ
definesK2As k2 = f(t_n + h/2, y_n + h k1 / 2) ⓘ
definesK3As k3 = f(t_n + h/2, y_n + h k2 / 2) ⓘ
definesK4As k4 = f(t_n + h, y_n + h k3) ⓘ
evaluatesFunctionPerStep 4 times ⓘ
hasGlobalErrorOrder 4 ⓘ
hasLocalTruncationErrorOrder 5 ⓘ
hasOrder 4 ⓘ
isAlsoKnownAs classical fourth-order Runge–Kutta method ⓘ
surface form: RK4

standard fourth-order Runge–Kutta method ⓘ
isConditionallyStable true ⓘ
isDescribedIn many numerical analysis textbooks ⓘ
isDeterministic true ⓘ
isExplicit true ⓘ
isMoreAccurateThan Euler’s method for numerical integration ⓘ
surface form: Euler method

second-order Runge–Kutta methods for same step size ⓘ
isNotAStiffSolver true ⓘ
isSelfStarting true ⓘ
isSuitableFor non-stiff ordinary differential equations ⓘ
isTradeOffBetween accuracy and computational cost ⓘ
isTypicallyImplementedWithFixedStepSize true ⓘ
isWidelyUsedIn computational biology ⓘ
control systems ⓘ
engineering simulations ⓘ
physics ⓘ
scientific computing ⓘ
requiresMoreFunctionEvaluationsThan Euler’s method for numerical integration ⓘ
surface form: Euler method
requiresSolvingAlgebraicEquations false ⓘ
solves initial value problems for ordinary differential equations ⓘ
stabilityDependsOn step size h and problem stiffness ⓘ
updateFormula y_{n+1} = y_n + h (k1 + 2 k2 + 2 k3 + k4) / 6 ⓘ
usesDependentVariable y ⓘ
usesIndependentVariable t ⓘ
usesIntermediateSlope k1 ⓘ
k2 ⓘ
k3 ⓘ
k4 ⓘ
usesNumberOfStages 4 ⓘ
usesStepSizeSymbol h ⓘ
usesTimeStepping discrete grid t_n = t_0 + n h ⓘ
usesWeightedAverageOfSlopes (k1 + 2 k2 + 2 k3 + k4) / 6 ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Euler’s method for numerical integration → isGeneralizedBy → classical fourth-order Runge–Kutta method ⓘ
Runge–Kutta methods → hasExample → classical fourth-order Runge–Kutta method ⓘ
classical fourth-order Runge–Kutta method → isAlsoKnownAs → classical fourth-order Runge–Kutta method ⓘ
this entity surface form: RK4