numerical_solution

• To: mathgroup at smc.vnet.net
• Subject: [mg73354] numerical_solution
• From: "j. r. campanha" <campanha at rc.unesp.br>
• Date: Tue, 13 Feb 2007 07:02:59 -0500 (EST)

```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] ==== 0.4, v[0] ==== 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] ==== 0.4, v[0] ==== 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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