2012-2013/TD_maple/TD_Euler/TDEuler.mw

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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8"># Procedure calculant une solution approch\303\251e de y'(t) = f(t,y(t)) par la m\303\251thode d'Euler</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">myEuler := proc (f, n, a, b, z0)
local tz, i, h;
h := (b-a)/n;
tz := array([seq([a+i*h, i], i = 0 .. n)]);
tz[1,2] := z0;
for i from 1 to n do
tz[i+1,2] := tz[i,2]+h*f(tz[i,1], tz[i,2]);
end do;
return tz;
end proc;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2J0kiZkc2IkkibkdGJUkiYUdGJUkiYkdGJUkjejBHRiU2JUkjdHpHRiVJImlHRiVJImhHRiVGJUYlQyc+OCYqJiwmOSciIiI5JiEiIkY0OSVGNj44JC1JJmFycmF5RyUqcHJvdGVjdGVkRzYjNyMtSSRzZXFHRjw2JDckLCZGNUY0KiY4JUY0RjBGNEY0RkUvRkU7IiIhRjc+JkY5NiRGNCIiIzkoPyhGRUY0RjRGN0kldHJ1ZUdGPD4mRjk2JCwmRkVGNEY0RjRGTCwmJkY5NiRGRUZMRjQqJkYwRjQtOSQ2JCZGOTYkRkVGNEZVRjRGNE9GOUYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8"># On va l'appliquer \303\240 l'\303\251quation f' = f</Font></Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">f := (t, x) -&gt; x ;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2JEkidEc2IkkieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlOSVGJUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">approx := myEuler(f, 100, 0, 10, 1):</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eulerPlot := plot(approx);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">exactPlot := plot(exp(x), x = 0..10, color = 'red');</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display(eulerPlot, exactPlot);</Text-field>
</Input>
<Output>
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</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8"># Procedure qui fournit la solution exacte de l'\303\251quation y'(t) = f(t,y(t))</Font></Text-field>
</Input>
</Group>
<Group labelreference="L146" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solExact := proc(f, z0)
local eq, CI, sol;
eq := diff(y(t),t) = f(t,y(t));
CI := y(0) = z0;
sol := dsolve({eq, CI}, y(t));
return subs(sol, y(t));
end;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2JEkiZkc2IkkjejBHRiU2JUkjZXFHRiVJI0NJR0YlSSRzb2xHRiVGJUYlQyY+OCQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUY2LTkkNiRGNkYzPjglLy1GNDYjIiIhOSU+OCYtSSdkc29sdmVHNiRGMUkoX3N5c2xpYkdGJTYkPCRGLUY7RjNPLUklc3Vic0dGMTYkRkJGM0YlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L147" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8"># Procedure qui va tracer les deux courbes sur le m\303\252me graphe</Font></Text-field>
</Input>
</Group>
<Group labelreference="L148" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">compareSol := proc(f, n, a, b, z0)
local approx, exact, plotApprox, plotExact;
approx := myEuler(f, n, a, b, z0);
plotApprox := plot(approx);
plotExact := plot(solExact(f, z0), t=a..b, color = 'red');
display(plotApprox, plotExact);
end;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2J0kiZkc2IkkibkdGJUkiYUdGJUkiYkdGJUkjejBHRiU2JkknYXBwcm94R0YlSSZleGFjdEdGJUkrcGxvdEFwcHJveEdGJUkqcGxvdEV4YWN0R0YlRiVGJUMmPjgkLUkobXlFdWxlckdGJTYnOSQ5JTkmOSc5KD44Ji1JJXBsb3RHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0YxPjgnLUY9NiUtSSlzb2xFeGFjdEdGJTYkRjVGOS9JInRHRiU7RjdGOC9JJmNvbG9yR0YlLkkkcmVkR0YlLV9JJnBsb3RzR0Y+SShkaXNwbGF5R0YlNiRGO0ZDRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L153" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">compareSol(f, 100, 1, 10, 3);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" 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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">f := (t,x) -&gt; exp(-t)*cos(10*t) - x;</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">compareSol(f, 100, 0, 2, 0);</Text-field>
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