您所在位置：主题：请大家帮我看看这个非线性方程组该怎么来解
sibo080302
[专家分：0] 发布于 2009-06-19 14:31:00
[size=3]本人现在做课题要解一个复杂的非线性方程组，对于matlab本人是个初学者，自己也编写了个matlab程序，可是不收敛，初值很不好给。我把自己编写的程序放在下面了，请大家不吝赐教！！谢谢了！！！
m文件内容：
function F=myfun(x)
global fr im k k1 m mu n r ri
for i=1:8
t0=1+6.28*(i-1)/(8*40)
a=(im/(mu*t0*r)-k1*r/mu)/k
F(i)=2*(a*x(i))^(9/10)+(9*k1/(10*k*mu))*(a*x(i))^(-1/10)*(2*r*x(9)+n*ri)...
-x(10)*cos(x(9)+0.785*(i-1));
end
sum=0.0;
sum1=0.0;
for i=1 : 8
nij=-m*(ri+r)*x(9)^2/2+k1*r*x(9)/mu+(im/(mu*r)-k1*r/mu)*x(i)+k1*n*ri...
/(2*mu);
noj=m*(ri+r)*x(9)^2/2+k1*r*x(9)/mu+(im/(mu*r)-k1*r/mu)*x(i)+k1*n*ri...
/(2*mu);
sum=sum+nij*sin(x(9)+(i-1)*0.785)+mu*nij*cos(x(9)+(i-1)*0.785)...
-k1*(ri*(n-x(9))-r*x(i))*cos(x(9)+(i-1)*0.785);
sum1=sum1+nij*cos(x(9)+(i-1)*0.785)-mu*nij*sin(x(9)+(i-1)*0.785)...
+k1*(ri*(n-x(9))-r*x(i))*sin(x(9)+(i-1)*0.785);
end
F(9)=sum;
F(10)=sum1-fr;
以下是我在命令窗口的内容：
k1=0.001
r=0.0065;
mu=0.15;
k=729455627;
m= 3.14 * r ^ 2 * 0.013 * 7.87 * 10 ^ 3;
im=m*r^2;
fr=1000;
ri=0.04225;
n=1000*6.28/60;
x0=[200;200;200;200;200;200;200;200;45;0.00001];
global fr im k k1 m mu n r ri;
options=optimset('display','iter','largescale','on');
[x,fval,exitflag,output]=fsolve(@myfun,x0,options)
下面是我的不收敛的结果：
Optimizer appears to be converging to a minimum that is not a root:
Sum of squares of the function values is > sqrt(options.TolFun).
Try again with a new starting point.
x =
201.8292
200.3597
198.6797
197.7723
198.1687
199.6367
201.3174
202.2272
44.5322
-0.0000
fval =
Columns 1 through 6
0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000
Columns 7 through 10
0.0000 0.0000 0.0011 -999.9929
exitflag =
-2
output =
firstorderopt: 0.9769
iterations: 13
funcCount: 154
cgiterations: 13
algorithm: 'large-scale: trust-region reflective Newton'
message: [1x169 char[/size]
m文件内容：
function F=myfun(x)
global fr im k k1 m mu n r ri
for i=1:8
t0=1+6.28*(i-1)/(8*40)
a=(im/(mu*t0*r)-k1*r/mu)/k
F(i)=2*(a*x(i))^(9/10)+(9*k1/(10*k*mu))*(a*x(i))^(-1/10)*(2*r*x(9)+n*ri)...
-x(10)*cos(x(9)+0.785*(i-1));
end
sum=0.0;
sum1=0.0;
for i=1 : 8
nij=-m*(ri+r)*x(9)^2/2+k1*r*x(9)/mu+(im/(mu*r)-k1*r/mu)*x(i)+k1*n*ri...
/(2*mu);
noj=m*(ri+r)*x(9)^2/2+k1*r*x(9)/mu+(im/(mu*r)-k1*r/mu)*x(i)+k1*n*ri...
/(2*mu);
sum=sum+nij*sin(x(9)+(i-1)*0.785)+mu*nij*cos(x(9)+(i-1)*0.785)...
-k1*(ri*(n-x(9))-r*x(i))*cos(x(9)+(i-1)*0.785);
sum1=sum1+nij*cos(x(9)+(i-1)*0.785)-mu*nij*sin(x(9)+(i-1)*0.785)...
+k1*(ri*(n-x(9))-r*x(i))*sin(x(9)+(i-1)*0.785);
end
F(9)=sum;
F(10)=sum1-fr;
以下是我在命令窗口的内容：
k1=0.001
r=0.0065;
mu=0.15;
k=729455627;
m= 3.14 * r ^ 2 * 0.013 * 7.87 * 10 ^ 3;
im=m*r^2;
fr=1000;
ri=0.04225;
n=1000*6.28/60;
x0=[200;200;200;200;200;200;200;200;45;0.00001];
global fr im k k1 m mu n r ri;
options=optimset('display','iter','largescale','on');
[x,fval,exitflag,output]=fsolve(@myfun,x0,options)
下面是我的不收敛的结果：
Optimizer appears to be converging to a minimum that is not a root:
Sum of squares of the function values is > sqrt(options.TolFun).
Try again with a new starting point.
x =
201.8292
200.3597
198.6797
197.7723
198.1687
199.6367
201.3174
202.2272
44.5322
-0.0000
fval =
Columns 1 through 6
0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000
Columns 7 through 10
0.0000 0.0000 0.0011 -999.9929
exitflag =
-2
output =
firstorderopt: 0.9769
iterations: 13
funcCount: 154
cgiterations: 13
algorithm: 'large-scale: trust-region reflective Newton'
message: [1x169 char[/size]