Question

matlab编写方程

各位大侠，我是个新手，对于编程语言可以说一窍不通。但是我现在急着要写出一个简单的方程求解。拜托大侠帮帮啊，我把仅有的两个麦片奉上了。

方程：d(Ct)/dt=k(Cmax-Ct)^2
其中：Ct=24.8 23.86667 23.27333 21.67333 18.48667 16.20667 13.93333 7.70667 5.98667 4.40667 1.59333 0.66667 0

t=0,1,6,12,18,24,30,36,42,48,54,60,72

Cmax=max(Ct)=24.8

ps:d(Ct)/dt一阶导数
求k

Answer 1

先求Ct-t的关系

y=dsolve('Dy-k*(24.8-y)^2=0')

 

y =

 

                           124/5

 124/5 - 1/(25*(C1+ (k*t)/25))

再用matlab拟合参数k和C1

t=[0,1,6,12,18,24,30,36,42,48,54,60,72]';

Ct=[24.8 23.86667 23.27333 21.67333 18.48667 16.20667 13.93333...

    7.70667 5.98667 4.40667 1.59333 0.66667 0]';

ft_ = fittype('124/5 - 1/(25*(C1 + (k*t)/25))',...

    'dependent',{'Ct'},'independent',{'t'},...

    'coefficients',{'k','C1'});

st=[-0.001 0.4]

[curve, goodness]= fit(t,Ct,ft_,'Startpoint',st)

figure,plot(t,Ct,'*'),hold on,

plot(curve,'predobs',0.99); 

st =

   -0.0010    0.4000

curve = 

     General model:

       curve(t) = 124/5 - 1/(25*(C1 + (k*t)/25))

     Coefficients (with 95% confidence bounds):

       k =   -0.001356  (-0.002203, -0.0005092)

       C1 =    0.005256  (0.003034, 0.007479)

goodness = 

           sse: 348.0195

       rsquare: 0.6773

           dfe: 11

    adjrsquare: 0.6480

          rmse: 5.6248