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'[2])/.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[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 > -- DrMajorBob at yahoo.com