How to plot multiple curves on the same screen for different values of "b" with bvp4c solver?

I am trying to draw multiple plots for multiple "b" values on a the same screen. The code is here. Any kind of help would be great.

function solution

b=1;

R=2;

pp=[1; 2; 3];

for i=1:numel(pp)

b=pp(i);

end

dYdX = @(X,Y) [Y(2); Y(3); (R/3*Y(2)).*(-2*Y(1).*Y(3)+Y(2)^.2)];

res = @(ya,yb) [ya(1)-b; ya(2); yb(2)];

SolYinit = bvpinit(linspace(0,100,1000),[0; 0; 0;]);

Fsol = bvp4c(dYdX, res, SolYinit);

X1 = Fsol.x;

Y1 = Fsol.y;

figure (1)

plot(X1, Y1(2,:), 'LineWidth', 2);

hold on

Answer 1

[Star Strider]

The problem is that the initial conditions are uniformly zero, so any change in ‘b’ will not be evident since the entire result will be zero otherwise. Also, the entire code needs to be inside the loop.

The ‘res’ function will inherit the value of ‘b’ from the workspace, so it does not have to be passed as an extra parameter, however it could be. It would then be:

res = @(ya,yb,b) [ya(1)-b; ya(2); yb(2)];

and the call too it in the bvp4c call would then be:

Fsol = bvp4c(dYdX, @(ya,yb)res(ya,yb,b), SolYinit);

That also works.

Try this —

b=1;
R=2; 
pp=[1; 2; 3];
for i=1:numel(pp)
    b=pp(i);
    dYdX = @(X,Y) [Y(2);  Y(3);  (R/3*Y(2)).*(-2*Y(1).*Y(3)+Y(2)^.2)];                     
    res = @(ya,yb) [ya(1)-b;  ya(2);  yb(2)];       
    SolYinit = bvpinit(linspace(0,100,1000),[0; 0; 0]+eps);    
    Fsol = bvp4c(dYdX, res, SolYinit);
    X1{i} = Fsol.x;
    Y1{i} = Fsol.y;
end

figure (1)
hold on
for k = 1:numel(pp)
    plot(X1{k}, Y1{k}(2,:), 'LineWidth', 2, 'DisplayName',sprintf('p = %d',pp(k)))
end
hold off
legend('Location','best')

The initial conditions need to be something other than zero in order that the output not be uniformly zero, so I added eps to nudge them away from zero.

.

[Torsten]

Y1 = b , Y2 = Y3 = 0 is the solution of the system. Initial conditions won't change this.

[Star Strider]

‘I am trying to draw multiple plots for multiple "b" values on a the same screen.’

The question is about plotting the curves, and changing the initial conditions slightly (and putting everything in the loop) allows the differences due to ‘b’ to be visible.

[Ke Le]

Agree. Thank you again.

[Star Strider]

As always, my pleasure!

Answer 2

[Torsten]

The solution will be

Y1 = b, Y2 = Y3 = 0

Is it that what you want ?

[Ke Le]

Yes, it is. Thank you @Torsten