       Re: NIntegrate and Plot solution of differ. equa. over initial conditions

• To: mathgroup at smc.vnet.net
• Subject: [mg124437] Re: NIntegrate and Plot solution of differ. equa. over initial conditions
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 19 Jan 2012 05:15:51 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```You didn't define "sol". You defined "sol[p,v]" when p and v are numeric.

Hence, NIntegrate[p*v*(v-y')/.sol,{p,0.1,1}] doesn't work because "sol"
is undefined.

You didn't give v a numeric value in that expression, either, so there's
no chance of sol[p, v] being defined.

Give your problem a lot more thought, until it actually makes sense.

Bobby

On Wed, 18 Jan 2012 04:59:51 -0600, Itzhak Shechtman
<shechtma at netvision.net.il> wrote:

> Hi all,
>
> I would be grateful for any help.
>
> I have the set of 2 ordinary differential equations:
>
>
> Clear[sol, q, k];
> B = 5.5*10^7;
> q[x_, y_] = 1 + 2 x + x^2 + y^2;
> k[x_, y_] = 2 (x/(1 + 2 x + x^2 + y^2))^0.5;
> sol[p_?NumericQ,v_
> ?NumericQ]:=NDSolve[{
>    x''[t]==
>       B*(2 (1 - k[x[t], y[t]]^2)*
>       EllipticK[k[x[t], y[t]]] - (2 - k[x[t], y[t]]^2*
>       (1+x[t]))* EllipticE[k[x[t], y[t]]])/(q[x[t],
>       y[t]]^1.5 k[x[t], y[t]]^2*(1 - k[x[t], y[t]]^2)),
>    y''[t] ==
>      B*2 y[t]*
>       EllipticE[k[x[t], y[t]]]/(q[x[t], y[t]]^1.5*(1 - k[x[t], y[t]]^2)),
>    x == p, x' == 0,
>    y'== v, y==-100000},
> {x, y}, {t, 0,2}];
>
> I wish to:
>
> 1) sol1=NIntegrate[p*v*(v-y')/.sol,{p,0.1,1}]; and
>
> 2) Plot[sol1,{v,10^3,10^5}]
> Mathematica does not accept it, objecting to solving the equations with
> non numeric initial conditions( p and v ), despite the above definition
> of sol.
>
> Does anyone have an idea?
> Thanks for the trouble.
>
> Itzhak
>

--
DrMajorBob at yahoo.com

```

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