why isn't my newton rhapson method giving me a quadratic conversion rate?

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Linnea
Linnea 2023-11-19
编辑： Torsten 2023-11-23
The code is running just fine, but the value konv(end)/(konv(end-1)^2) intended to show (e(i+1)/(e(i)^2)) gives an answer of 9.9952e+07, which seems to indicate that the conversion rate isn't quadratic. Is there something obviously wrong with the code? Help appreciated.
%constants
d=0.007;
dI=1.219;
Rfi=1.76*(10^(-4));
Rf0=Rfi;
hs=356;
ht=hs;
kw=60;
dTm=29.6;
Q=801368;
Aex=64.15;
a=((1/ht)+Rfi)/dI;
b=log(d/dI)/(2*kw);
c=d*(a+b)+Rf0+(1/hs);
A=((1/ht)+Rfi)/dI;
B=(log(d/dI)+1)/2*kw;
f=c*(Q/dTm)-Aex;
df=(Q/dTm)*(A+B);
%d1-do ska va mindre än tol
%i slutet av iterationen
%så man kan sätta while
d=0.007;
d0=d;
d1=10;
abs(d1-d0);
iteration=0;
konv=[0]
while abs(d1-d0)>10^(-8);
a=((1/ht)+Rfi)/dI;
b=log(d/dI)/(2*kw);
c=d*(a+b)+Rf0+(1/hs);
f=c*(Q/dTm)-Aex;
A=((1/ht)+Rfi)/dI;
B=(log(d/dI)+1)/2*kw;
df=(Q/dTm)*(A+B);
d0=d;
d1=d-f/df;
d=d1;
iteration=iteration+1;
konv=[konv, abs(d1-d0)];
end
konv(end)/(konv(end-1)^2)
iteration
d

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回答（1 个）

Torsten
Torsten 2023-11-19
编辑：Torsten 2023-11-19
If
b=log(d/dI)/(2*kw);
instead of
b=log(d/dI)/2*kw;
as was first written in your previous code, then B must also be
B=(log(d/dI)+1)/(2*kw);
instead of
B=(log(d/dI)+1)/2*kw;
In other words: df is wrong because B is wrong.
  6 个评论
显示 4更早的评论
Linnea
Linnea 2023-11-21
could you please repeat what exactly you did? i changed B to B=(log(d/dI)+1)/(2*kw); but it's still giving me 20 000 iterations.
Torsten
Torsten 2023-11-21
编辑：Torsten 2023-11-23
Ran in:
Replace
%B=(log(d/dI)+1)/2*kw;
by
%B=(log(d/dI)+1)/(2*kw);
in the above code you posted. Nothing else is necessary.
%constants
d=0.007;
dI=1.219;
Rfi=1.76*(10^(-4));
Rf0=Rfi;
hs=356;
ht=hs;
kw=60;
dTm=29.6;
Q=801368;
Aex=64.15;
a=((1/ht)+Rfi)/dI;
b=log(d/dI)/(2*kw);
c=d*(a+b)+Rf0+(1/hs);
A=((1/ht)+Rfi)/dI;
B=(log(d/dI)+1)/2*kw;
f=c*(Q/dTm)-Aex;
df=(Q/dTm)*(A+B);
%d1-do ska va mindre än tol
%i slutet av iterationen
%så man kan sätta while
d=0.007;
d0=d;
d1=10;
abs(d1-d0);
iteration=0;
konv=[];
while abs(d1-d0)>10^(-10);
a=((1/ht)+Rfi)/dI;
b=log(d/dI)/(2*kw);
c=d*(a+b)+Rf0+(1/hs);
f=c*(Q/dTm)-Aex;
A=((1/ht)+Rfi)/dI;
B=(log(d/dI)+1)/(2*kw);
df=(Q/dTm)*(A+B);
d0=d;
d1=d-f/df;
d=d1;
iteration=iteration+1;
konv=[konv, abs(d1-d0)];
end
for i = 2:numel(konv)
konv(i)/konv(i-1)^2
end
ans = 17.0397
ans = 9.7667
ans = 9.1463
ans = 9.1980
iteration
iteration = 5
d
d = 0.0191

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