Euler’s method for numerical integration

E54272

explicit method first-order method initial value problem solver numerical method one-step method

Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.

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All labels observed (4)

Label	Occurrences
Euler method	5
Euler’s method	2
Euler’s method for numerical integration canonical	1
forward Euler method	1

Statements (50)

Predicate	Object
instanceOf	explicit method ⓘ first-order method ⓘ initial value problem solver ⓘ numerical method ⓘ one-step method ⓘ
accuracyDependsOn	step size h ⓘ
alsoKnownAs	Euler’s method for numerical integration ⓘ surface form: Euler’s method Euler’s method for numerical integration ⓘ surface form: forward Euler method
appliedIn	engineering computations ⓘ physics simulations ⓘ population dynamics models ⓘ
approximates	solution curve of dy/dt = f(t,y) ⓘ
assumes	given initial condition y(t0) = y0 ⓘ
convergenceOrder	1 ⓘ
doesNotRequire	solving algebraic equations at each step ⓘ
errorType	accumulated round-off error ⓘ truncation error ⓘ
geometricInterpretation	uses tangent line approximation at each step ⓘ
globalErrorOrder	O(h) ⓘ
hasUpdateFormula	y_{n+1} = y_n + h f(t_n, y_n) ⓘ
input	differential equation dy/dt = f(t,y) ⓘ initial time t0 ⓘ initial value y0 ⓘ step size h ⓘ
isExplicit	true ⓘ
isGeneralizedBy	Heun’s method ⓘ classical fourth-order Runge–Kutta method ⓘ higher-order Runge–Kutta methods ⓘ improved Euler method ⓘ midpoint method ⓘ
isNotWellSuitedFor	stiff differential equations ⓘ
isRelatedTo	backward Euler method ⓘ predictor–corrector methods ⓘ semi-implicit Euler method ⓘ
isSpecialCaseOf	Runge–Kutta methods ⓘ linear multistep methods with one step ⓘ
isSuitableFor	non-stiff differential equations ⓘ
localTruncationErrorOrder	O(h^2) ⓘ
namedAfter	Leonhard Euler ⓘ
output	discrete approximation (t_n, y_n) to solution ⓘ
requires	evaluation of derivative function f at current point ⓘ
smallerStepSizeEffect	increases accuracy ⓘ increases computational cost ⓘ
stabilityType	conditionally stable ⓘ
timeSteppingDirection	forward in time ⓘ
typicalUse	simple simulations where high accuracy is not critical ⓘ teaching basic concepts of numerical ODE solving ⓘ
usedFor	approximating solutions of ordinary differential equations ⓘ numerical integration of initial value problems ⓘ
uses	step size h ⓘ