while loop convergence for sum

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Magnus 2014-12-16

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https://ww2.mathworks.cn/matlabcentral/answers/166862-while-loop-convergence-for-sum

评论： Magnus 2014-12-16

Dear all,

I'm using a while loop in order to find a value etapl iteratively. The code looks like follows where eta(:) is a first guess (which is close to the desired solution). For N=3 it seems to work but for N>5 the solution doesnt converge but jumps between two values. It doesnt appear to be an issue with the initial values X.

for jj=1:dp % looking for a number dp of etapl
etapl=eta(jj); %assign etapl to the first guess
eta_old=etapl+0.01; %introduce an error to go into the while loop
while abs(etapl-eta_old) > 0.001  % convergence criterion
eta_old = etapl; 
sum_eta=0;
for n=2:2:N-1 % a sum from n=2,4,... to N-1 that contains etapl
   sum_eta=sum_eta+sinh(n*pi/X(1)*(d+etapl))*(X(n)*...
       cos(n*pi/X(1)*x(jj))+X(n+1)*sin(n*pi/X(1)*x(jj))); 
end
etapl=Psi/(X(1)/T-U)-1/(X(1)/T-U)*sum_eta;
end
eta(jj)=etapl;
end

Any assistance is very much appreciated!

Kind regards,

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Star Strider 2014-12-16

What are T and U? Maybe I’m missing something, but I don’t see them in the code you posted. They might be important.

Magnus 2014-12-16

在 MATLAB Online 中打开

Hey, I'm sorry. If you want to run the code they might be helpful.

T=1;
N=5; %can be changed to any other odd number but then extend the X(n) by any %value smaller than the values before, i.e. X(n+1)<<X(n)
U=0;
dp=100;
Psi=0; % or any small value e.g. 1e-2
X(1)=1.5506;
x=linspace(0,X(1),dp);
eta=0.01/2*cos(2*pi/X(1)*x(jj)); %for initial guess
X(2)=0.0013;
X(3)=8.2545e-2
X(4)=0.001e-3
X(5)=0.001e-3