Finding average step size and slope with ode45

I want to be able to calculate the average step size and slope for each value in the loop.

I first want to plot the log values of dT and TOL.

I believe my average step size (dT) should be the average of 1/T.

t = [0, 5]; % time span

y0 = 1; % initial condition

dy0 = 2; % initial condition first derivative

dydt = @(t,y) [y(2); ((1 - y(1)^2))*y(2) - y(1)];

for j = 1:10

TOL(j) = 1*exp(-1-j);

options = odeset('AbsTol',TOL(j),'RelTol',TOL(j));

[T{j},Y{j}] = ode45(dydt, t, [y0, dy0], options);

dT = mean(1/length(T)); % average step size

plot(log(dT),log(TOL));

hold on;

grid

j = j+1;

end

hold off;

Errors I'm facing:

• my plot doesn't show up
• my slope receives the error 'Undefined function 'log' for input arguments of type 'cell'.'
• not sure if I am thinking of average step size correctly

Side note: Would I be able to generate multiple slopes using polyfit in one graph?

Answer 1

[Star Strider]

Subscript ‘dT’ as well. The code will be more efficient if you move the plot outside the loop:

t = [0, 5];    % time span
y0 = 1;         % initial condition
dy0 = 2;     % initial condition first derivative
dydt = @(t,y) [y(2); ((1 - y(1)^2))*y(2) - y(1)];

for j = 1:10
    TOL(j) = 1*exp(-1-j);
    options = odeset('AbsTol',TOL(j),'RelTol',TOL(j));
    [T{j},Y{j}] = ode45(dydt, t, [y0, dy0], options);
    
    dT(j) = mean(1/length(T)); % average step size    
end

figure
plot(log(dT),log(TOL));
grid

[Star Strider]

Changing the name of ‘dT’ isn’t necessary. You just need to subscript it as ‘dT(j)’ to create a vector from it. The plot then shows up for me with the code I posted.

Re-posting:

t = [0, 5];    % time span
y0 = 1;         % initial condition
dy0 = 2;     % initial condition first derivative
dydt = @(t,y) [y(2); ((1 - y(1)^2))*y(2) - y(1)];

for j = 1:10
    TOL(j) = 1*exp(-1-j);
    options = odeset('AbsTol',TOL(j),'RelTol',TOL(j));
    [T{j},Y{j}] = ode45(dydt, t, [y0, dy0], options);
    dT(j) = mean(1/length(T)); % average step size    
end

figure
plot(log(dT),log(TOL));
grid

EDIT —

The plot shows up when I run my code, although the plot image doesn’t seem to be appearing when I post it here. I am attaching it as well to work around that problem.

[EB]

I realized my error.

Thanks again!!

[Star Strider]

As always, my pleasure!