Plotting for various values of the same parameter on the same plot

Asking here on how to plot "Y1(2,:)" for multiple "S" values on the same figure?. Consider values such as "S=0.1, 0.5, 1.1, 1.5" etc.

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

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

SolYinit = bvpinit(linspace(0,5,50),[0; 0.2; 0.4]);

Fsol = bvp4c(dYdX, res, SolYinit);

X1 = Fsol.x;

Y1 = Fsol.y;

figure (1)

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

hold on

[Ive J]

hold on, have you tried hold on?

[Ke Le]

@Ive J Yes, it doesn't show it there, however, I've tried it there. Even with "hold on", I am looking for help on plotting for various "S" values. Any help will be appreciated.

Answer 1

[Star Strider]

Set ‘S’ as a vector, add ‘S’ as an additional parameter to the ‘dYdX’ function, then iterate through the values of ‘S’.

Try this —

Sv = [0.1, 0.5, 1.1, 1.5];
dYdX = @(X,Y,S) [Y(2);  Y(3);  S*Y(2).^2+Y(1).*Y(3)];  
res = @(ya,yb) [ya(1)-1;  ya(2);  yb(2)];                  
SolYinit = bvpinit(linspace(0,5,50),[0; 0.2; 0.4]);

for k = 1:numel(Sv)
    S = Sv(k);
    Fsol = bvp4c(@(X,Y)dYdX(X,Y,S), res, SolYinit);
    X1{k} = Fsol.x;
    Y1{k} = Fsol.y;
end
 
figure (1)
Nrsp = numel(Sv);
for k = 1:Nrsp
    subplot(Nrsp,1,k)
    plot(X1{k}, Y1{k}(2,:), 'LineWidth', 2)
    grid
    title(sprintf('S = %.1f',Sv(k)))
end

I opted for the subplots because the scales vary so significantly on the solutions that the details in the solution for ‘S(1)’ gets lost if they are all plotted on the same axes.

.

[Ke Le]

That's really amazing sa far. Love to see it coming. Why I get the error message on my machine, though, I run in R2021a which is same as yours. Try to sort it out, kindly. Many thanks.

"Unable to perform assignment because brace indexing is not supported for variables of this type.

Error in test (line 9)

X1{k} = Fsol.x;"

[Star Strider]

The only reason I can think of that could have thrown that error is that you preallocated ‘X1’ and ‘Y1’ as matrices (rather than as cell arrays) prior to the loop, or have them defined as matrices (rather than as cell arrays) somewhere else earlier.

One way to avoid the error is to call them something else, such as ‘Xc’ and ‘Yc’ in the loop (and in the following plot loop), again providing that those variables have also not been previously defined as something else earlier in the code.

There could be other reasons, however that is the only situation that I have ever encountered a similar error in my experience. In any event, giving them unique names will likely solve it.

.

[Ke Le]

Thanks

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

Answer 2

[the cyclist]

% Some data
x = 1:10;

% Create the figure window, use the hold command
% to prevent overwriting of axes
figure
hold on

% Plot line with different slope parameters
for s = 1:3
    plot(x,s*x)
end

[Ke Le]

@the cyclist How should we treat the above system for S values such as "-0.1, 0.5, 1.1, 1.5"?