# Question:Error: Newton iteration is not converging..

## Question:Error: Newton iteration is not converging..

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))^(1/3)+(3032/405)*r+(1/9*(-(2/15)*(8807640902+1170*sqrt(24475122685023))^(1/3)-7064468/(15*(8807640902+1170*sqrt(24475122685023))^(1/3))-1576/15))*r^2+(2/27*((13/90)*(8807640902+1170*sqrt(24475122685023))^(1/3)+22959521/(45*(8807640902+1170*sqrt(24475122685023))^(1/3))+5467/45))*r^3+(1/18*(-(1/15)*(8807640902+1170*sqrt(24475122685023))^(1/3)-3532234/(15*(8807640902+1170*sqrt(24475122685023))^(1/3))-893/15))*r^4+(2/45*((1/90)*(8807640902+1170*sqrt(24475122685023))^(1/3)+1766117/(45*(8807640902+1170*sqrt(24475122685023))^(1/3))+469/45))*r^5, 2 < r, (8/6075)*(2*(8807640902+1170*sqrt(24475122685023))^(2/3)+7064468+1651*(8807640902+1170*sqrt(24475122685023))^(1/3))/(8807640902+1170*sqrt(24475122685023))^(1/3));

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And the PDE is here,

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))));

z:=1000;

IC:={Phi(r,0)=Piinitial,D[2](Phi)(r,0)=0,D[1](Phi)(0,t)=0,D[1](Phi)(1000,t)=0}:
pds2:=pdsolve(pde1,IC,numeric,time=t,spacestep=0.1,range=0..1000);
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Now, when I try to plot the evolution of the system at time say ,,t=10 it returns the following error message,

Error, (in pdsolve/numeric/plot) unable to compute solution for t>.299999999999999989:
Newton iteration is not converging

I am new to maple and don't know how to handle this error.. is there anyway to demand maple to try and avoid newton maple or use some other method..

I would be grateful for any suggestions thanks.. Please find teh maple code here.maple_prime(help).mw

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