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Title Kinetic_ave
Parameters k1[0,100], k2[0,100];
Variable t, C;

StartProgram
var i:integer;

begin
for i:=0 to DataLength -1 do begin
      if i ==0
         C=0;
         else
      C:=C[i-1]+k1*(t-t[i-1])*exp(-0.2779*t) - k2*C*(t-t[i-1]);
         end;
EndProgram;
Data;
//t    C
   0    xxx
   1    xxx
   2    xxx
   4    xxx
   6    xxx
   10  xxx
   15  xxx
   24  xxx


Matlab´úÂ룺
function ODE_ave
clear all;clc
format long
aveall;
t=T_h(;
yexp=OLEave(;

k0=[1 1];  

y0=0;
lb=[0 0];
ub=[+inf +inf];   
yy=[y0 yexp'];

tspan=0:1:24;

[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc,k0,lb,ub,[],tspan,y0,yexp);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\t´ýÄâºÏ²ÎÊý k1 = %.6f\n',k(1))
fprintf('\t´ýÄâºÏ²ÎÊý k2 = %.6f\n',k(2))
fprintf(' \t²Ð²îƽ·½ºÍ= %.6f\n\n',resnorm)
ts=0:1:24;

[ts ys]=ode45(@KineticsEqs,ts,y0,[],k);
[ttt XXsim] = ode45(@KineticsEqs,tspan,y0,[],k);
y=XXsim(2:end);
xexp=yexp;
R2=1-sum((xexp-y).^2)./sum((xexp-mean(y)).^2);
fprintf('\n\t¾ö¶¨ÏµÊýR-Square = %.6f',R2);
figure(1)
plot(ts,ys,'b',tspan,yy,'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');
yr=y-yexp;
figure(2)
plot(tspan(2:end),yr,'r*',[-1 15],[0 0]),axis([-1 15 -0.5 0.5]);
figure(3)
plot(yexp,y,'ro',[21 29],[21 29],'b-');
(×÷ͼÕâ¿é¶ùÊÇcopyµÄ£¬Ã»ÓÐ×öÐÞ¸Ä)
%---------------------------------------------------------
function f = ObjFunc(k,tspan,y0,yexp)           
[t Xsim] = ode45(@KineticsEqs,tspan,y0,[],k) ;
ysim = Xsim(2:end);
size(ysim);
size(yexp);
f=ysim(1,1)+ysim(2,1)+ysim(4,1)+ysim(6,1)+ysim(10,1)+ysim(15,1)+ysim(24,1) - sum(yexp(:,1));
%----------------------------------------------------------

function dydt = KineticsEqs(t,y,k)
beta(1)=k(1);
beta(2)=k(2);
dydt = beta(1)*exp(-0.2779*t)-beta(2)*y;

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Parameters k1[0,100], k2[0,100];
Variable t, C;
InitialODEValue t=0,c=0;
ODEFunction c'=k1*exp(-0.2779*t)-k2*c;
Data;
//t    C
   0    xxx
   1    xxx
   2    xxx
   4    xxx
   6    xxx
   10  xxx
   15  xxx
   24  xxx
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Parameters k1, k2;
Variable t, C;
InitialODEValue t=0,c=0;
ODEFunction c'=k1*exp(-0.2779*t)-k2*c;
Data;
//t    C
   0    xxx
   1    xxx
   2    xxx
   4    x ...

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Variable x, y;
ODEFunction y'= k1*(0.701*exp(-3.211*x)+0.299*exp(-0.067*x))-k2*y;
Data;
//x, y
0         0
0.33      0.061043
1         0.03675
2         0.05932
4         0.095993
6         0.072057
10        0.05085
15        0.04678
24        0.047673
30        0.034973
48        0.030375
72        0

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Variable x, y;
ODEFunction y'= k1*(0.701*exp(-3.211*x)+0.299*exp(-0.067*x))-k2*y;
Data;
  ...

ÕâÊÇÃâ·ÑµÄÊÔÓð棬ÄãÕâ±»È˺öÓÆÁ˰¡£¬×îаæÒѾ­µ½9.0ÁË£¬¶øÇÒÖ»ÄÜÈ¥¹ÙÍø¹ºÂò¡£


¾ù·½²î(RMSE): 0.0171691634594409
²Ð²îƽ·½ºÍ(SSR): 0.00324258191286701
Ïà¹ØÏµÊý(R): 0.802484090026993
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.64398071474645
ÐÞÕýRƽ·½(Adj. R^2): 0.554975893433063
È·¶¨ÏµÊý(DC): 0.468028249120648
Fͳ¼Æ(F-Statistic): 23.5213130305514

²ÎÊý                  ×î¼Ñ¹ÀËã
--------------------        -------------
k1        0.13256115104059
k2        0.358504426638858

====== ½á¹ûÊä³ö ======

Îļþ: Êý¾ÝÎļþ-1
No        x        Ä¿±ê y        ¼ÆËã y
1        0.33        0.061043        0.0298491702527491
2        1        0.03675        0.053602315170092
3        2        0.05932        0.0683875960100214
4        4        0.095993        0.079360928514414
5        6        0.072057        0.0789300799888936
6        10        0.05085        0.0667093831255373
7        15        0.04678        0.0492934543907035
8        24        0.047673        0.02721397228202
9        30        0.034973        0.0182160615899268
10        48        0.030375        0.00545427669955797
11        72        0        0.00109238646097193
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