using shooting method for coupled ode

Hi all,

please help,I'm looking to solve the following system of equations with boundary conditions using the shooting method:

The equation and m-file attached .

I've found the solution using the BVP4C solver but need to also be able to find the solution using the shooting method.

I'm really quite new to MATLAB and don't really know where to start!

Any help anyone can give me would be greatly appreciated. Thanks!

[darova]

Can you rewrite this part?

function f= projfun(x,y)        
        f= [y(2)
            y(1)*y(3)+x*y(2)*y(3)+y(1)*y(2)+(y(9)*(1/alfa*Pr*x))-(y(2)/x)-(y(1)/(x*x))
            (-1/x)*(4*y(3)+y(2)+(y(1)/x))
            4*y(3)*y(3)+((x*y(3)+y(1)-(1/x))*((-1/x)*(4*y(3)+y(2)+(y(1)/x))))
            y(6)
            Pr*x*y(3)*y(6)+Pr*y(1)*y(6)-(y(6)/x)
            y(8)
            (1/B*Tinf)*(alfa*Pr*y(1)*y(8)+alfa*Pr*x*y(3)*y(8)-(((DT*Bs*Fiinf)/(Tinf*Dfi))*((Pr*x*y(3)*y(6)+Pr*y(1)*y(6)-(y(6)/x))-(y(6)/x))))
            y(9)
            ];
    end

To make it look like:

function f= projfun(x,y)        
E
E = y(1);
dE = y(2);
F = y(3);
dF = y(4);
% ...
f = zeros(9,1);
f(1) = dF;
f(2) = long_expr1;
f(3) = long_expr2;
% ...
end

1. Use variable instead of y(1),y(2) for long code
2. Why not define f function as you did before?

example

[1 - 2; 2]  % work
[1 -2; 2]   % doesn't work

I can't check your function because it's difficult to read. I don't want to write new one

Answer 1

[darova]

Thank you more readable code

Here are some mistakes

Some note:

Shouldn't last equations be like this? What is g? There is no g in your equations

% g  = y(7);
E = y(7);
dE  = y(8);
% dy(7) = dg;
dy(7) = -1*(4*E+df+f);                          % E'
dy(8) = (4*E*E)+((E*x+f-1)*(-1*(4*E+df+f)));    % E''

I also suggest you not to use global: LINK

You can just use nested functions

function proj
    % global variables - no need
    % code
    function dy = projfun(x,y)
        % global variables - no need
        % code
    end
end

[T K]

OK,Doctor darova thanks and appreciation .

I have modified all the errors that you mentioned ,

It remains an error only for the Variable g', please help me .

How to write the definition of g' in the function f'' ???

  E  = y(7);
        dE = y(8);
        g  = y(9);      %is it coorect for the definition of g'??
        dy(1) = df;
        dy(2) = (E*f)+(E*x*df)+(f*df)+((alfa*Pr*dg/(rho)))-(df)-f;   %is it coorect for definition of g'??
        dy(3) = dt;
        dy(4) = (Pr*dt*E)+(Pr*f*dt)-(dt);
        dy(5) = dc;
        dy(6) = (1/(B*Tinf))*((alfa*Pr*dc*f)+(alfa*Pr*E*x*dc)-(((DT*Bs*Fiinf)/(Tinf*Dfi))*(dt+dy(4))))-(dc);
        dy(7) = -1*(4*E+df+f);
        dy(8) = (4*E*E)+((E*x+f-1)*(-1*(4*E+df+f)));
        dy(9)=dg;    %is it coorect for the definition of g'??

[darova]

But what is g? Looks like it's constant. If it exists the previous version was correct also

[T K]

The variable g is not constant. But the question about definition g 'in its equation f'' and y (9) is

[T K]

And dy(9) Please help me Dr darova??

[darova]

It's ok i think. I tried ode45 to see how results can look like

[x,y] = ode45(@projfun,[0 1],y0);
plot(x,y)
str = strsplit(sprintf('y%d ',1:9),' ');
legend(str)

I did my best. Don't know how proceed

[T K]

Sorry for your effort, Doctor darova Finally, you can send me the program with the ODE45 that I mentioned in the drawing

[darova]

I tried to reduce timespan

m = linspace(0,1);

[T K]

Finally, please doctor darova The code has been successfully created and given ode45 format and bvp4c function ??? First solution y0 = [1 0 1 1 1 1 1 1 0]; % Pr = 4; % [x,y] = ode45(@projfun,[0 .1],y0); % plot(x,y) % str = strsplit(sprintf('y%d ',1:9),' '); % legend(str)

Second solution options = bvpset('stats','on','RelTol',1e-4); m = linspace(0,1); solinit = bvpinit(m,y0);

[darova]

[darova]

[T K]

Thank you very much Doctor Best vote

[darova]

Don't forget about thumb up

[darova]

How can i trust you?

[T K]

There is no problem and I am very happy for you