Difference between revisions of "NSolveODE Command"
From GeoGebra Manual
Noel Lambert (talk | contribs) (Created page with "<noinclude>{{Manual Page|version=4.2}}</noinclude> {{command|function}} ;NSolveODE[ <List of Derivatives>, <Initial x-coordinate>, <List of Initial y-coordinates>, <Final x-co...") |
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| − | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|function}} |
| − | {{command|function}} | + | ;NSolveODE( <List of Derivatives>, <Initial x-coordinate>, <List of Initial y-coordinates>, <Final x-coordinate> ) |
| − | ;NSolveODE | ||
:Solves (numerically) the system of differential equations | :Solves (numerically) the system of differential equations | ||
{{Example|1=<div> | {{Example|1=<div> | ||
| Line 7: | Line 6: | ||
:<code>g'(t, f, g, h) = h</code> | :<code>g'(t, f, g, h) = h</code> | ||
:<code><nowiki>h'(t, f, g, h) = -t h + 3t g + 2f + t</nowiki></code> | :<code><nowiki>h'(t, f, g, h) = -t h + 3t g + 2f + t</nowiki></code> | ||
| − | :<code><nowiki>NSolveODE | + | :<code><nowiki>NSolveODE({f', g', h'}, 0, {1,2,-2}, 10)</nowiki></code> |
| − | :<code><nowiki>NSolveODE | + | :<code><nowiki>NSolveODE({f', g', h'}, 0, {1,2,-2}, -5)</nowiki></code> (solves the system backwards in time).</div>}} |
{{Example|1=<div> | {{Example|1=<div> | ||
:<code>x1'(t, x1, x2, x3, x4) = x2</code> | :<code>x1'(t, x1, x2, x3, x4) = x2</code> | ||
| Line 18: | Line 17: | ||
:<code>x30 = 1.8</code> | :<code>x30 = 1.8</code> | ||
:<code>x40 = -1.5</code> | :<code>x40 = -1.5</code> | ||
| − | :<code>NSolveODE | + | :<code>NSolveODE({x1', x2', x3', x4'}, 0, {x10, x20, x30, x40}, 20)</code></div>}} |
{{Example|1=<div> Pendulum: | {{Example|1=<div> Pendulum: | ||
:<code>g = 9.8</code> | :<code>g = 9.8</code> | ||
| Line 26: | Line 25: | ||
:<code>y1'(t, y1, y2) = y2</code> | :<code>y1'(t, y1, y2) = y2</code> | ||
:<code>y2'(t, y1, y2) = (-g) / l sin(y1) </code> | :<code>y2'(t, y1, y2) = (-g) / l sin(y1) </code> | ||
| − | :<code>NSolveODE | + | :<code>NSolveODE({y1', y2'}, 0, {a, b}, 20) </code> |
| − | :<code>len = Length | + | :<code>len = Length(numericalIntegral1) </code> |
| − | :<code>c = Slider | + | :<code>c = Slider(0, 1, 1 / len, 1, 100, false, true, true, false) </code> |
| − | :<code>x1 = l sin(y(Point | + | :<code>x1 = l sin(y(Point(numericalIntegral1, c))) </code> |
| − | :<code>y1 = -l cos(y(Point | + | :<code>y1 = -l cos(y(Point(numericalIntegral1, c))) </code> |
:<code>A = (x1, y1) </code> | :<code>A = (x1, y1) </code> | ||
| − | :<code>Segment | + | :<code>Segment((0, 0), A)</code> |
| − | :<code>StartAnimation | + | :<code>StartAnimation()</code> |
</div>}} | </div>}} | ||
{{Note|1= See also [[SlopeField Command|SlopeField command]], [[SolveODE Command|SolveODE command]].}} | {{Note|1= See also [[SlopeField Command|SlopeField command]], [[SolveODE Command|SolveODE command]].}} | ||
Latest revision as of 09:37, 9 October 2017
- NSolveODE( <List of Derivatives>, <Initial x-coordinate>, <List of Initial y-coordinates>, <Final x-coordinate> )
- Solves (numerically) the system of differential equations
Example:
f'(t, f, g, h) = gg'(t, f, g, h) = hh'(t, f, g, h) = -t h + 3t g + 2f + tNSolveODE({f', g', h'}, 0, {1,2,-2}, 10)NSolveODE({f', g', h'}, 0, {1,2,-2}, -5)(solves the system backwards in time).
Example:
x1'(t, x1, x2, x3, x4) = x2x2'(t, x1, x2, x3, x4) = x3x3'(t, x1, x2, x3, x4) = x4x4'(t, x1, x2, x3, x4) = -8x1 + sin(t) x2 - 3x3 + t^2x10 = -0.4x20 = -0.3x30 = 1.8x40 = -1.5NSolveODE({x1', x2', x3', x4'}, 0, {x10, x20, x30, x40}, 20)
Example:
Pendulum:
g = 9.8l = 2a = 5(starting location)b = 3(starting force)y1'(t, y1, y2) = y2y2'(t, y1, y2) = (-g) / l sin(y1)NSolveODE({y1', y2'}, 0, {a, b}, 20)len = Length(numericalIntegral1)c = Slider(0, 1, 1 / len, 1, 100, false, true, true, false)x1 = l sin(y(Point(numericalIntegral1, c)))y1 = -l cos(y(Point(numericalIntegral1, c)))A = (x1, y1)Segment((0, 0), A)StartAnimation()
Note: See also SlopeField command, SolveODE command.
