vish

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These are questions asked by vish

I have the numerical solution of Phi(r,t) which is a numerical solution of a pde..

I want to find the following energy integral at fixed time say t=10 ,

Energy = int(a*r^2*Phi(r,10)^2 + 2*b*r*Phi(r,10)^3,r=0..infinity)... I could not find help in maple.. I guess I had to do the following

 

1. select the numerical solution dependent only on r at t=10 slice..

2.Use numerical methods to evaluate the integral..

 

This is the Pde I am trying to solve, with the initial profile function at t=0 called Piinitial, and IC=initialconditions,boundary conditions,

Piinitial := piecewise(r <= 1, (1/9)*r^2+(1/12150)*(31*(8807640902+1170*sqrt(24475122685023))^(2/3)+109499254+22553*(8807640902+1170*sqrt(24475122685023))^(1/3))/(8807640902+1170*sqrt(24475122685023))^(1/3), r <= 2 and 1 < r, (4/405)*(8807640902+1170*sqrt(24475122685023))^(1/3)*r+(14128936/405)*r/(8807640902+1170*sqrt(24475122685023...

This is the eq I am trying to solve

pde1:= diff(Phi(r,t),t,t) = (-(diff(Phi(r, t), r, r))*r^2-2*(diff(Phi(r, t), r))*r+2*(diff(Phi(r, t), r))^2+4*(diff(Phi(r, t), r))*(diff(Phi(r, t), r, r))*r+2*(diff(Phi(r, t), t, r))^2*r^2)/(r*(-r+2*r*(diff(Phi(r, t), r, r))+4*(diff(Phi(r, t), r))));

with initial conditions..

z=1000;

IC:={Phi(r,0)=Piinitial,D[2](Phi)(r,0)=0,D[1](Phi)(0,t)=0,D[1](Phi)(z,t)=0}:

pdsolve runs and returns the module..

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