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Overflow problem implementing Euler's method

POSTED BY: Athanasios Paraskevopoulos
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I can not do the comparison of two graphs like that
POSTED BY: Athanasios Paraskevopoulos

Yes, that problem has been solved. I am so grateful for your help. Both of you
POSTED BY: Athanasios Paraskevopoulos

You can probably simplify things by vectorizing your code.

Instead of doing everything in triplicate and having lots of code repetition, you can perhaps just do this:

\[Alpha] = 0.9;
\[Beta] = 0.2;
\[Gamma] = 0.4;

f[{x_, y_, z_}] := {z + (y - \[Alpha])*x, 1 - \[Beta]*y - x^2, -x - \[Gamma]*z}

Q[a_, b_, c_, h_, NN_] := (
 u[0] = {a, b, c};
 Do[
   u[n + 1] = u[n] + h*f[u[n] + h/2*f[u[n]]],
   {n, 0, NN}]);

Q[1, 3, 2, 0.1, 200];
X = Interpolation[Table[{n, u[n]}, {n, 0, 2000}]];
ParametricPlot3D[X[t], {t, 0, 2000}]
POSTED BY: Arnoud Buzing

Ok, thanks. But is not wrong the code above right?
POSTED BY: Athanasios Paraskevopoulos

Your code is fine, just trying to show you how to make it potentially simpler.
POSTED BY: Arnoud Buzing

Thank you very much! I will keep it in mind!
POSTED BY: Athanasios Paraskevopoulos

Is it possible to contrast on the same axis system the two ParametricPlots from the first two cases on the [0,200]?
POSTED BY: Athanasios Paraskevopoulos

Yes, for example with this code:

MakePlot[{\[Alpha]_, \[Beta]_, \[Gamma]_}, {a_, b_, c_}, h_, max_Integer] := Module[{u, if},
  f[{x_, y_, z_}] := {z + (y - \[Alpha])*x, 1 - \[Beta]*y - x^2, -x - \[Gamma]*z};
  u[0] = {a, b, c};
  Do[u[n + 1] = u[n] + h*f[u[n] + h/2*f[u[n]]], {n, 0, max}];
  if = Interpolation[Table[{n, u[n]}, {n, 0, max/h}]];
  ParametricPlot3D[if[t], {t, 0, 2000}]
]

You can do this:

plot1 = MakePlot[{0.9, 0.2, 1.2}, {1, 3, 2}, 0.1, 200]
plot2 = MakePlot[{0.9, 0.2, 0.4}, {1, 3, 2}, 0.1, 200]

And then combine them:

Show[{plot1, plot2}]
POSTED BY: Arnoud Buzing
POSTED BY: Athanasios Paraskevopoulos

Here is another idea, using AnimationVideo. Same MakePlot function, but with an explicit PlotRange to keep that constant for any parameter choice:

MakePlot[{\[Alpha]_, \[Beta]_, \[Gamma]_}, {a_, b_, c_}, h_, 
  max_Integer] := Module[{u, if},
  f[{x_, y_, z_}] := {z + (y - \[Alpha])*x, 
    1 - \[Beta]*y - x^2, -x - \[Gamma]*z};
  u[0] = {a, b, c};
  Do[u[n + 1] = u[n] + h*f[u[n] + h/2*f[u[n]]], {n, 0, max}];
  if = Interpolation[Table[{n, u[n]}, {n, 0, max/h}]];
  ParametricPlot3D[if[t], {t, 0, 2000}, 
   PlotRange -> {{-3, 3}, {-3, 3}, {-3, 3}}]
  ]

Then:

AnimationVideo[
 MakePlot[{0.9, 0.2, t}, {1, 1, 1}, 0.02, 1000],
 {t, 0.0, 2.0}]

Generates this video:

https://www.wolframcloud.com/obj/2d831a2f-4c28-4881-82bc-3bc95c88bbad
POSTED BY: Arnoud Buzing

Amazing!!! Could I do the same for the

Plot[{X[t],Y[t],Z[t]},{t,0,200},PlotLegends->"Expressions"]
POSTED BY: Athanasios Paraskevopoulos

I have tried to do what you have advised me. Could you take a look please and tell me your opinion? Thank you in advance.

POSTED BY: Athanasios Paraskevopoulos

Not sure what opinion you're looking for, but that looks beautiful to me?

Problem solved?
POSTED BY: Arnoud Buzing
POSTED BY: Henrik Schachner
POSTED BY: Arnoud Buzing
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