WOLFRAM

Wolfram Language & System Documentation Center

MaxStepSize

is an option to functions like NDSolve that specifies the maximum size of a single step used in generating a result.

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

MaxStepSize

MaxStepSize

is an option to functions like NDSolve that specifies the maximum size of a single step used in generating a result.

Details

Examples

open all close all

Basic Examples  (1)

Keep the largest step taken by NDSolve to be 0.01:

Wolfram Language code: NDSolve[{x''[t] + x[t] == Exp[-1000(t - π) ^ 2], x[0] == x'[0] == 0}, x, {t, 0, 20}, MaxStepSize -> 0.01]
Wolfram Language code: Plot[Evaluate[First[x[t] /. %]], {t, 0, 20}]

Applications  (2)

The default step control may miss a suddenly varying feature:

Wolfram Language code: Plot[Evaluate[(y[x] /. NDSolve[{y''[x] + (1 + Sech[1000 (x - Pi)]) y[x] == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 10}]) - Cos[x]], {x, 0, 10}]

A smaller MaxStepSize setting ensures that NDSolve catches the feature:

Wolfram Language code: Plot[Evaluate[(y[x] /. NDSolve[{y''[x] + (1 + Sech[1000 (x - Pi)]) y[x] == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 10}, MaxStepSize -> 0.01]) - Cos[x]], {x, 0, 10}]

Attempting to compute the number of positive integers less than misses several events:

Wolfram Language code: Block[{n = 0}, NDSolve[{y'[t] == y[t], y[-1] == E^-1}, y, {t, 5}, Method -> {"EventLocator", "Event" -> Sin[π y[t]], "EventAction" :> n++}];n]

Setting a small enough MaxStepSize ensures that none of the events are missed:

Wolfram Language code: Block[{n = 0}, NDSolve[{y'[t] == y[t], y[-1] == E^-1}, y, {t, 5}, MaxStepSize -> 0.001, Method -> {"EventLocator", "Event" -> Sin[π y[t]], "EventAction" :> n++}];n]

Properties & Relations  (1)

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

Wolfram Language code: msf = NDSolve[{y''[x] + (1 + Sech[1000 (x - Pi)]) y[x] == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 10}, MaxStepFraction -> 1 / 1000]
Wolfram Language code: mss = NDSolve[{y''[x] + (1 + Sech[1000 (x - Pi)]) y[x] == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 10}, MaxStepSize -> 10 1 / 1000]
Wolfram Language code: msf === mss
Wolfram Research (1996), MaxStepSize, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxStepSize.html.

Text

Wolfram Research (1996), MaxStepSize, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxStepSize.html.

CMS

Wolfram Language. 1996. "MaxStepSize." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaxStepSize.html.

APA

Wolfram Language. (1996). MaxStepSize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaxStepSize.html

BibTeX

@misc{reference.wolfram_2026_maxstepsize, author="Wolfram Research", title="{MaxStepSize}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/MaxStepSize.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_maxstepsize, organization={Wolfram Research}, title={MaxStepSize}, year={1996}, url={https://reference.wolfram.com/language/ref/MaxStepSize.html}, note=[Accessed: 12-June-2026]}