Plot titles in subplots for various initial conditions

Hello. I have this code below and i need to put the four different values of y0 in each subplot title. How do i do this ? Is it possible to be done in one of the for loops ?

clc, clear all, close all

%--- Solving the diff. eqn. y'(t) = y(t) - c*y^2(t) with c = 0.5 using
%--- Euler's method and ode45 and comparing in same graph. I have four
%--- initial values for y0

tmax = 100;
y0 = [0.1 0.5 1.0 2.0];
f = @(t,y) y - 0.5*y.^2;
h = 0.1;
t = [0:tmax];
n = length(t)-1;
y = zeros(1,n);

for i = 1:length(y0)
    [T,Y] = ode45(f,[0 tmax],y0(i));
    subplot(2,2,i), plot(T,Y,'o'), hold on
        for j = 1:n
            y(1) = y0(i);
            y(1,j+1) = y(j) + h*f(':',y(j));
        end
    subplot(2,2,i), title('y'' = y - 0.5y^2, y_0 = 0.1'), plot(t,y),legend('Exact','Euler','Location','Best'), xlabel('t'), ylabel('y')
end

Answer 1

[Manikanta Aditya]

Hi @Left Terry,

You can modify the subplot titles dynamically within the loop by using the current value of y0(i).

clc, clear all, close all
%--- Solving the diff. eqn. y'(t) = y(t) - c*y^2(t) with c = 0.5 using
%--- Euler's method and ode45 and comparing in same graph. I have four
%--- initial values for y0
tmax = 100;
y0 = [0.1 0.5 1.0 2.0];
f = @(t,y) y - 0.5*y.^2;
h = 0.1;
t = [0:tmax];
n = length(t)-1;
y = zeros(1,n);
for i = 1:length(y0)
    [T,Y] = ode45(f,[0 tmax],y0(i));
    subplot(2,2,i), plot(T,Y,'o'), hold on
        for j = 1:n
            y(1) = y0(i);
            y(1,j+1) = y(j) + h*f(':',y(j));
        end
    subplot(2,2,i), title(['y'' = y - 0.5y^2, y_0 = ', num2str(y0(i))]), plot(t,y), legend('Exact','Euler','Location','Best'), xlabel('t'), ylabel('y')
end

In this modified code, the title function within the for loop dynamically sets the title for each subplot to include the corresponding initial condition ( y_0 ). The num2str function converts the numerical value of ( y_0(i) ) to a string so it can be included in the title.

I hope this helps you.

[Left Terry]

@Manikanta Aditya I think the sprintf(...) version worked better for me. Why did you edited your answer ? Was there a mistake ?

[Manikanta Aditya]

@Left Terry, No no nothing is wrong, this is another way, I found, so updated with this.

Please find the 'sprintf' version below:

clc, clear all, close all
% Solving the diff. eqn. y'(t) = y(t) - c*y^2(t) with c = 0.5 using
% Euler's method and ode45 and comparing in the same graph. I have four
% initial values for y0
tmax = 100;
y0 = [0.1 0.5 1.0 2.0];
f = @(t,y) y - 0.5*y.^2;
h = 0.1;
t = [0:tmax];
n = length(t)-1;
y = zeros(1,n);

for i = 1:length(y0)
    [T,Y] = ode45(f,[0 tmax],y0(i));
    subplot(2,2,i), plot(T,Y,'o'), hold on
    for j = 1:n
        y(1) = y0(i);
        y(1,j+1) = y(j) + h*f(':',y(j));
    end
    titleStr = sprintf('y'' = y - 0.5y^2, y_0 = %.1f', y0(i)); % Create dynamic title
    subplot(2,2,i), title(titleStr), plot(t,y), legend('Exact','Euler','Location','Best'), xlabel('t'), ylabel('y')
end

• The sprintf function is used to create a string that includes the current initial value y0(i) for each subplot title.
• The title function is updated to use this dynamically created string.

Answer 2

[Naga]

To include the different values of y0 in each subplot title, you can modify the title within the loop to dynamically include the current y0 value. You can achieve this by using the num2str function to convert the numerical value to a string and then concatenate it into the title.

clc, clear all, close all
%--- Solving the diff. eqn. y'(t) = y(t) - c*y^2(t) with c = 0.5 using
%--- Euler's method and ode45 and comparing in same graph. I have four
%--- initial values for y0
tmax = 100;
y0 = [0.1 0.5 1.0 2.0];
f = @(t,y) y - 0.5*y.^2;
h = 0.1;
t = [0:tmax];
n = length(t)-1;
y = zeros(1,n);

for i = 1:length(y0)
    [T,Y] = ode45(f,[0 tmax],y0(i));
    subplot(2,2,i), plot(T,Y,'o'), hold on
    
    for j = 1:n
        y(1) = y0(i);
        y(1,j+1) = y(j) + h*f(':',y(j));
    end
    
    % Update the title to include the current y0 value
    subplot(2,2,i), title(['y'' = y - 0.5y^2, y_0 = ', num2str(y0(i))]), ...
    plot(t,y), legend('Exact','Euler','Location','Best'), xlabel('t'), ylabel('y')
end

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