Can Yvv and Yuu be embedded in the program

Can Yvv and Yuu be embedded in the program

The formulas above without Yvv and Yuu Matlab：edit， Then，the following lines between the percent sign (%) copied to m.file, save %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function dx=myfun(t,x) dx(1)=-6*x(2)*x(2)-9; dx(2)=-3*x(1)*x(2)-2*x(3); dx(3)=x(1)*x(2)+x(3)+8; dx=dx(:); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Matlab： x0=[3,-4,2]; t0=0:0.1:10; [t,x]=ode45('myfun',[0,2],x0); plot(t,x) legend('u','v','Y')

[Torsten]

According to your MATLAB code, the third equation reads

u*v+Y+8=Ydot,

not

u*v+Y+8=vdot

Which version is correct ?

Best wishes

Torsten.

[Lan]

u*v+Y+8=vdot

[Torsten]

In this case, add equations (2) and (3).

You get

4*u*v + 3Y + 8 = 0,

thus

Y=-4/3*u*v-8/3.

So only solve equations (1) and (2) and calculate Y as

Y=-4/3*u*v-8/3

Best wishes

Torsten.

[Lan]

Thanks for your answer! Then, How can the values of Yvv and Yuu be embedded in the program ?

[Torsten]

function dx=myfun(t,x)

t_array=[0 1 2 3 4 5 6 7 8 9 10];
Y_uu_array=[6 7 4 10 2 3 5 4 9 6 8];
Y_vv_array=[1 5 3 10 11 8 2 6 8 10 3];

Y_uu=interp1(t_array,Y_uu_array,t);
Y_vv=interp1(t_array,Y_vv_array,t);

dx=zeros(2,1);

u=x(1);
v=x(2);
Y=-(4*u*v+8)/3;
dx(1)=-6*v^2-9;
dx(2)=-3*u*v-2*Y-Y_uu-Y_vv;

Best wishes

Torsten.

[Lan]

Thank you! Happy Chinese New Year!恭喜发财！哈哈！

[Torsten]

Thank you.

One small error in the code I posted:

Replace

Y=-(4*u*v+8)/3;

by

Y=-(4*u*v+8+Y_uu+Y_vv)/3;

Formerly, I used the equations without Y_uu and Y_vv to calculate Y.

Best wishes

Torsten.