       Re: numerical_solution

• To: mathgroup at smc.vnet.net
• Subject: [mg73369] Re: numerical_solution
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 14 Feb 2007 05:20:26 -0500 (EST)
• Organization: Uni Leipzig
• References: <eqsa2a\$jmb\$1@smc.vnet.net>

```Hi,

you can't know, because the solution has two numerical errors,
from rounding and more important from the method.
Since NDSolve[] has an local error control it should
keep the local error smaller than 10^(-PrecisionGoal) and
since it does it with both version the numerical quality
of the solutions is the same. If you don't have additional
information like "I wish to conserve the energy." or something
else solutions are equivalent.

But the runtime may be different for different methods and you
should use the method that offer the best performance.

Regards
Jens

j. r. campanha wrote:
> Dear MathGroup people
>
>
> How can I know which is the best numerical solution?
>
>
> w == 6;
> A == 0.1;
> B == 0.17;
> F == 0.501;
>
> solution1 == NDSolve[{x'[t] ==== v[t], v'[t] ==== -(B)*(v[t]) - (A)*(((x[t]=
> ))/(1 - (x[t])^2)) + (F)*(Cos[w*t]),x ==== 0.4, v ==== 0.3}, {x, v}, =
> {t, 260, 270}];
>
> ParametricPlot[Evaluate[{x[t], v[t]} /. solution1], {t, 260, 270}, Frame ->=
>  True]
>
>
> OR
>
> solution2 == NDSolve[{x'[t] ==== v[t], v'[t] ==== -(B)*(v[t]) - (A)*(((x[t]=
> ))/(1 - (x[t])^2)) + (F)*(Cos[w*t]),x ==== 0.4, v ==== 0.3}, {x, v}, =
> {t, 260, 270}, Method -> StiffnessSwitching];
>
>
> ParametricPlot[Evaluate[{x[t], v[t]} /. solution2], {t, 260, 270}, Frame ->=
>  True]
>
>
>
> Jose R. Campanha
> UNESP-Physics Dpto
> Rio Claro - S=E3o Paulo
> Brasil
>
>

```

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