Heun’s method

E300767
Runge–Kutta method numerical integration method ordinary differential equation solver

Heun’s method is a second-order Runge–Kutta numerical integration technique that improves on Euler’s method by using a predictor-corrector approach to achieve greater accuracy.

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All labels observed (4)

Label Occurrences
Heun method 1
Heun’s method canonical 1
improved Euler method 1

Statements (42)

Predicate Object
instanceOf Runge–Kutta method ⓘ
numerical integration method ⓘ
ordinary differential equation solver ⓘ
advantage better accuracy than Euler for same step size ⓘ
alsoKnownAs explicit trapezoidal rule ⓘ
Heun’s method ⓘ
surface form: improved Euler method

Heun’s method ⓘ
surface form: modified Euler method
appliesTo initial value problems for ordinary differential equations ⓘ
basedOn Euler’s method for numerical integration ⓘ
surface form: Euler’s method
belongsToFamily explicit two-stage Runge–Kutta methods ⓘ
canBeExtendedTo adaptive step-size control ⓘ
category one-step ODE integration method ⓘ
comparedToEuler achieves second-order accuracy instead of first-order ⓘ
requires one additional function evaluation per step ⓘ
computesIntermediateValue y_tilde = y_n + h f(t_n, y_n) ⓘ
correctorSlopeComputation average of initial and predicted slopes ⓘ
disadvantage higher computational cost per step than Euler ⓘ
firstStageDescription predictor step using Euler’s method ⓘ
globalErrorOrder O(h^2) ⓘ
goal improve accuracy over Euler’s method ⓘ
implementationComplexity simple ⓘ
isExplicit true ⓘ
isSingleStepMethod true ⓘ
localTruncationErrorOrder O(h^3) ⓘ
namedAfter Karl Heun ⓘ
numericalQuadratureAnalogy trapezoidal rule for integrating derivative over a step ⓘ
order second-order ⓘ
relatedMethod classical fourth-order Runge–Kutta method ⓘ
Runge–Kutta methods ⓘ
surface form: midpoint Runge–Kutta method
requires evaluation of right-hand side function f(t,y) ⓘ
secondStageDescription corrector step using average of slopes ⓘ
stability more stable than explicit Euler for many problems ⓘ
stageCount 2 ⓘ
stepType two-stage Runge–Kutta scheme ⓘ
timeStepping fixed step size in basic form ⓘ
typicalUse solving non-stiff ordinary differential equations ⓘ
updateFormula y_{n+1} = y_n + h/2 [ f(t_n, y_n) + f(t_n + h, y_tilde ) ] ⓘ
usedIn applied mathematics education ⓘ
engineering simulations ⓘ
scientific computing ⓘ
uses predictor–corrector approach ⓘ
usesSlopeEvaluationsPerStep 2 ⓘ

Referenced by (4)

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

Euler’s method for numerical integration → isGeneralizedBy → Heun’s method ⓘ
Runge–Kutta methods → hasExample → Heun’s method ⓘ
this entity surface form: Heun method
Heun’s method → alsoKnownAs → Heun’s method ⓘ
this entity surface form: improved Euler method
Heun’s method → alsoKnownAs → Heun’s method ⓘ
this entity surface form: modified Euler method