2楼: Originally posted by wjx0162 at 2011-11-08 09:03:25:
两边取对数，把指数方程变为代数方程，直接求代数方程的根。

4楼: Originally posted by wjx0162 at 2011-11-08 15:10:03:
那也一样，两边取对数，先把指数方程变为代数方程，然后用数据点拟合待定系数D的代数方程，最后求出D

1楼: Originally posted by feifei_ney at 2011-11-08 08:41:40:
有个迁移模型方程

已知MF,∞=9.18mg,Lp=0.009,
MF,t与t的一组相关实验数据如下所示
t               MF,t
7200        3.28265
86400        5.57149
345600        6.84803
864 ...

function AA
D0=3.55e-15;
%D0=3.55e-19;
% options = optimset('Algorithm','interior-point');
% [D,fval,flag] = fmincon(@fei,D0,[],[],[],[],0,[],[],options)
[D,resnorm,residual,exitflag,output,lambda,jacobian] = lsqnonlin(@fei,D0,0,[],[])

function F=fei(D)
Lp=0.009;
s=[];
A=[7200        3.28265
86400        5.57149
345600        6.84803
864000        7.47618
7.776e6       9.17744];
t=A(:,1);
MFt=A(:,2);
MF=9.18;
Lp=0.009;
y=1-MFt/MF;
k=0:100000;
for i=1:length(t)
s(i)=sum(8./(pi*(2*k+1)).^2.*exp(-D*(pi*(2*k+1)).^2*t(i)^2/(4*Lp^2)));
end
s
F=sum((y-s').^2);

function AA
D0=3.55e-15;
%D0=3.55e-19;
% options = optimset('Algorithm','interior-point');
% [D,fval,flag] = fmincon(@fei,D0,[],[],[],[],0,[],[] ... [/quote]


[code]function AA
D0=3.55e-15;%给需要计算的D一个迭代计算的初值
%D0=3.55e-19;%给需要计算的D一个其他迭代计算的初值
% options = optimset('Algorithm','interior-point');
% [D,fval,flag] = fmincon(@fei,D0,[],[],[],[],0,[],[],options)%去掉这三行的%将用另外算法fmincon求D
[D,resnorm,residual,exitflag,output,lambda,jacobian] = lsqnonlin(@fei,D0,0,[],[])%采用lsqnonlin算法求D
%====编写函数关于D的方程======
function F=fei(D)
%===========赋值====
Lp=0.009;
s=[];
A=[7200        3.28265
86400        5.57149
345600        6.84803
864000        7.47618
7.776e6       9.17744];
t=A(:,1);
MFt=A(:,2);
MF=9.18;
Lp=0.009;
y=1-MFt/MF;
%=========计算无穷级数（用前100000项逼近）===
k=0:100000;
for i=1:length(t)
s(i)=sum(8./(pi*(2*k+1)).^2.*exp(-D*(pi*(2*k+1)).^2*t(i)^2/(4*Lp^2)));
end
%=======显示无穷级数计算结果====
s
%====构造需要优化的函数（1-MFt/MF与无穷级数的差的平方和）=======
F=sum((y-s').^2);