WOLFRAM

Wolfram Language & System Documentation Center

MaxStepFraction

is an option to functions like NDSolve that specifies the maximum fraction of the total range to cover in a single step.

Examples  
Basic Examples  
Applications  
Properties & Relations  
See Also
History
Cite this Page

MaxStepFraction

MaxStepFraction

is an option to functions like NDSolve that specifies the maximum fraction of the total range to cover in a single step.

Examples

open all close all

Basic Examples  (1)

Make sure that NDSolve uses at least 100 steps over the integration range:

Wolfram Language code: NDSolve[{x''[t] + x[t] == Exp[-1000(t - π) ^ 2], x[0] == x'[0] == 0}, x, {t, 0, 20}, MaxStepFraction -> 1 / 100]
Wolfram Language code: Plot[Evaluate[First[x[t] /. %]], {t, 0, 20}]

Applications  (1)

Features with small relative size in the integration interval can be missed:

Wolfram Language code: Table[Plot[Evaluate[y[x] /. NDSolve[{y''[x] + y[x] == Exp[-(1000 (x / L - 1 / 3)) ^ 2], y[0] == y'[0] == 0}, y, {x, L}]], {x, L / 4, L / 2}, PlotRange -> All], {L, {1, 10, 100, 1000}}]

Use MaxStepFraction to ensure features are not missed, independent of interval size:

Wolfram Language code: Table[Plot[Evaluate[y[x] /. NDSolve[{y''[x] + y[x] == Exp[-(1000 (x / L - 1 / 3)) ^ 2], y[0] == y'[0] == 0}, y, {x, L}, MaxStepFraction -> 0.001]], {x, L / 4, L / 2}, PlotRange -> All], {L, {1, 10, 100, 1000}}]

Properties & Relations  (1)

For an interval length l, MaxStepFraction->f is equivalent to MaxStepSize->(f l):

Wolfram Language code: msf = NDSolve[{x''[t] + x[t] == Exp[-1000(t - π) ^ 2], x[0] == x'[0] == 0}, x, {t, 0, 20}, MaxStepFraction -> 1 / 100];
Wolfram Language code: mss = NDSolve[{x''[t] + x[t] == Exp[-1000(t - π) ^ 2], x[0] == x'[0] == 0}, x, {t, 0, 20}, MaxStepSize -> (20 1 / 100)];
Wolfram Language code: msf === mss
Wolfram Research (1999), MaxStepFraction, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxStepFraction.html.

Text

Wolfram Research (1999), MaxStepFraction, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxStepFraction.html.

CMS

Wolfram Language. 1999. "MaxStepFraction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaxStepFraction.html.

APA

Wolfram Language. (1999). MaxStepFraction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaxStepFraction.html

BibTeX

@misc{reference.wolfram_2026_maxstepfraction, author="Wolfram Research", title="{MaxStepFraction}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/MaxStepFraction.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_maxstepfraction, organization={Wolfram Research}, title={MaxStepFraction}, year={1999}, url={https://reference.wolfram.com/language/ref/MaxStepFraction.html}, note=[Accessed: 12-June-2026]}