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[0] == p, x'[0] == 0,
y'[0]== v, y[0]==-100000},
{x, y}, {t, 0,2}];
I wish to:
1) sol1=NIntegrate[p*v*(v-y'[2])/.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