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

• To: mathgroup at smc.vnet.net
• Subject: [mg124392] NIntegrate and Plot solution of differ. equa. over initial conditions
• From: Itzhak Shechtman <shechtma at netvision.net.il>
• Date: Wed, 18 Jan 2012 05:59:51 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```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

```

• Prev by Date: Re: MatrixPower problem
• Next by Date: Problem Integrating a sequence of polynomials
• Previous by thread: How to set up Intel C++ Composer XE for Mathematica on windows 7?
• Next by thread: Re: NIntegrate and Plot solution of differ. equa. over initial conditions