Defining 2N ODEs with 2N variables when using ode45
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I am new to Matlab and am using it to complete a university project. I am trying to solve a system of 2N ODEs for the position of N vortices in a 2D fluid. They interact with each other and have a circulation strenth Γ, and each vortex has a location given by the
and
coordinate for each index (See below the system of ODEs). I am able to set up the equations explicitly with a couple of 'for' loops but am struggling to figure out how to define each equation when it is in a 'function' environment and without a nested 'for' loop.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1418298/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1418303/image.png)
Each vortex has an initial position for x,y which I have each stored in 2 Nx1 vectors and I want to define each differential equation in terms of x and y as shown in the screenshot below (note the prime on the sum denotes an ommision of the α= β term). I also am trying to use ode45 to solve these and then plot the output which I am able to do, it's just the defining of the ODEs where I am stuck.
Hope this makes sense and thanks in advance for any help.![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1418308/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1418308/image.png)
5 commentaires
Torsten
le 23 Juin 2023
Modifié(e) : Torsten
le 23 Juin 2023
I meant that ODE45 spent so much effort computing the solution and you just carelessly overwrite it :-)
function dzdt = vortex_pos(t,z)
N = numel(z)/2;
x = z(1:N);
y = z(N+1:end);
dzdt = zeros(2*N,1);
%% ODEs
for i = 1:N
for j = setdiff(1:N, i)
dzdt(i) = dzdt(i) + (-1/(2*pi))*(gamma(j)*(y(i)-y(j))/((x(i)-x(j))^2 + (y(i)-y(j))^2));
dzdt(N+i) = dzdt(N+i) + (1/(2*pi))*(gamma(j)*(x(i)-x(j))/((x(i)-x(j))^2 + (y(i)-y(j))^2));
end
end
end
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