Solving ODEs with different sets of initial conditions
12 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Amir Kleiner
am 13 Nov. 2018
Kommentiert: Torsten
am 15 Nov. 2018
I have a system of ODEs which I solve using ode45.
In my case, I am interested in solving the same equation hundreds and even thousands of times, each time with slightly different randomly generated initial conditons, as follows (the sovled function is just an example):
n_times = 1000;
t_i = 1; t_f = 10; tspan = [t_i,t_f];
for i = 1:n_times
y0 = randn(2, 1);
[t, y] = ode45(@(t,y) harmosc(t,y), tspan, y0);
end
function dy = harmosc(t,y)
dy = zeros(size(y));
dy(1)=y(2);
dy(2)=-y(1);
end
In my current code I run a loop for all the initial conditions, but this is rather slow for the large amount of time I have to solve the equations. I have tried solving this entering the initial conditions as a matrix instead of looping over a vector, something like:
n_times = 1000;
t_i = 1; t_f = 10; tspan = [t_i,t_f];
y0 = randn(2, n_times);
[t, y] = ode45(@(t,y) harmosc(t,y), tspan, y0);
function dy = harmosc(t,y)
dy = zeros(size(y));
dy(1,:)=y(2,:);
dy(2,:)=-y(1,:);
end
But this doesn't work - I manage to get a y vector of the wrong size ([length(t), 2*n_times]), and with only one solution (y(1,:), y(2,:)) while all other columns of the matrix are just some constant.
Does someone know how this can be done correctly?
I am aware of the fact that the loop results in better accuracy of the solution, but that's a price I'm willing to pay for the reduced time in the "matrix" way.
Thanks!
0 Kommentare
Akzeptierte Antwort
Torsten
am 14 Nov. 2018
function main
n_times = 1000;
t_i = 1; t_f = 10; tspan = [t_i,t_f];
y0 = randn(2, n_times);
y0 = reshape(y0, 2*n_times, 1);
[t, y] = ode45(@(t,y) harmosc(t,y,n_times), tspan, y0);
y = reshape(y,size(y,1),2,n_times)
plot(t,y(:,1,15),t,y(:,2,15))
end
function dy = harmosc(t,y,n_times)
y = reshape(y,2,n_times);
dy = zeros(size(y));
dy(1,:)=y(2,:);
dy(2,:)=-y(1,:);
dy = reshape(dy,2*n_times,1);
end
2 Kommentare
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Ordinary Differential Equations finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!