fsolve 已停止,因为当前步长的相对大小小于 步长容差的平方的值,但按照函数容差的值衡量, 函数值向量不接近于零。

clc;clear;
syms x1 x2;
G=1e18;
k=1.38064852e-23;
h=6.62606896e-34;
pi=3.141592654;
e=1.6021892e-19;
m0=9.11e-31;
T=1000+273.15;
E0=3.507; a=9.09e-4; b=830;
Eg=E0-a*T^2/(b+T);
mc=0.2;
mv=1.5;
Ns=4.4e28;
vn=sqrt(3*k*T/mc/m0);
vp=sqrt(3*k*T/mv/m0);
cn1=1e-15*vn;cp1=1e-18*vp;
cn3=5e-19;cp3=5e-23;
cn2=1e-18*vn;cp2=1e-15*vp;
BB=1e-15;
CAugn=1e-31;CAugp=1e-31;
Nv = 2 *(2 * pi * mv * m0 * k * T)^1.5/(h^3);
Nc = 2 * (2 * pi * mc * m0 * k * T)^1.5/(h^3);
ni2=Nc.*Nv.*exp(-Eg.*e./k./T);
dE=x1-x2;
w=1/(1+exp(-dE*e/k/T));
n=Nc.*(w*exp((x1-Eg).*e./k./T)+(1-w)*exp((x2-Eg).*e./k./T));
p=Nv.*(w*exp(-x2.*e./k./T)+(1-w)*exp(-x1.*e./k./T));
EfD=w.*x1+(1-w).*x2;
EfA=w.*x2+(1-w).*x1;
MgEt=0.26;
Mg0=1*Ns*exp(-1.875*e/k/T);
Mg1=1*Ns.*exp(-(2.132-EfA).*e./k./T);
VNEt31=0.48;VNEt10=3.31;
VN0=1*Ns*exp(-3.486*e/k/T);
VN1=1*Ns.*exp(-(0.178+EfD).*e./k./T);
VN3=1*Ns.*exp(-(-0.781+3*EfD).*e./k./T);
UBB=BB*(n.*p-ni2);
UAug=(CAugn*n+CAugp*p).*(n.*p-ni2);
USMg1=Mg1.*(n.*p-ni2)./((1/(cp2.*vp)).*(n+Nc.*exp((MgEt-Eg).*e./k./T))+(1/(cn2.*vn)).*(p+Nv.*exp(-MgEt.*e./k./T)));
USVN1=VN1.*(n.*p-ni2)./((1/(cp1.*vp)).*(n+Nc.*exp((VNEt10-Eg).*e./k./T))+(1/(cn1.*vn)).*(p+Nv.*exp(-VNEt10.*e./k./T)));
USVN3=VN3.*(n.*p-ni2)./((1/(cp3.*vp)).*(n+Nc.*exp((VNEt31-Eg).*e./k./T))+(1/(cn3.*vn)).*(p+Nv.*exp(-VNEt31.*e./k./T)));
f1(x1,x2)=p+3*VN3+VN1-Mg1-n;
f2(x1,x2)=G-UBB-UAug-USMg1-USVN1-USVN3;
f=[f1 f2];
func = matlabFunction(f, 'Vars',{[x1, x2]});
[x,fval]= fsolve(func,[0.75,1.4])
No solution found. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared, but the vector of function values is not near zero as measured by the value of the function tolerance.
x = 1×2
0.9795 0.9795
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fval = 1×2
1.0e+17 * 0.0000 -1.3082
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对于这段代码最后的输出是找不到解,fsolve 已停止,因为当前步长的相对大小小于 步长容差的平方的值,但按照函数容差的值衡量, 函数值向量不接近于零。要如何优化得到数值解

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Asked:

on 15 Oct 2025

Edited:

on 24 Oct 2025

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