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Help With ODEs Solver(ode45)

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function [] = call_func
clear all
close all
tspan = [ 0 10 ]
y0 = 0:0.01:1;
x0 = 0:0.01:1;
theta0 = 0:pi/5:2*pi;
l = 1;
options=odeset('RelTol',1e-8,'AbsTol',1e-8)
for k = 1:length(y0)
for s = 1:length(x0)
for w = 1:length(theta0)
[t,x] = ode45(@func,tspan,[x0(s) y0(k) theta0(w)],options);
%legend('b = blue', 'r = red')
if (max(mod(x(:,1),l))<0.5) && (min(mod(x(:,2),l))>0.5)
c='r.';
else
c='b.';
end
plot(mod(x(end,1),l),mod(x(end,2),l),c);
hold on
end
end
end
end
function dydt = func(t,x)
Vs = 0.095;% true value
alpha =1; % true value
dydt = [sin(2*pi*x(1))*cos(2*pi*x(2))+Vs*cos(x(3))
-cos(2*pi*x(1))*sin(2*pi*x(2))+Vs*sin(x(3))
2*pi*(-alpha*cos(2*pi*x(1))*cos(2*pi*x(2))*sin(x(3))+sin(2*pi*x(1))*sin(2*pi*x(2)))];
end
I use this code to analyze a fluid system. The problem is it take sometimes up to 20 mintues to get results. Does anyone know if there is a way to solve and get the plot a quicker way?

Accepted Answer

David Goodmanson
David Goodmanson on 12 Mar 2021
Edited: David Goodmanson on 12 Mar 2021
Hi Ahmed,
repeating the plot command every time in the nested for loops is not helping, For a smaller case (I didn't want to wait for 20 minutes), the following code plots once and cuts the time down by about a factor of 5:
clear all
close all
tspan = [ 0 10 ]
y0 = 0:0.01:.1;
x0 = 0:0.01:.1;
theta0 = 0:pi/5:2*pi;
l = 1;
options=odeset('RelTol',1e-8,'AbsTol',1e-8);
Xr = zeros(length(x0),length(y0),length(theta0));
Yr = zeros(length(x0),length(y0),length(theta0));
Xb = zeros(length(x0),length(y0),length(theta0));
Yb = zeros(length(x0),length(y0),length(theta0));
%tic
for k = 1:length(y0)
for s = 1:length(x0)
for w = 1:length(theta0)
[t,x] = ode45(@func,tspan,[x0(s) y0(k) theta0(w)],options);
%legend('b = blue', 'r = red')
if (max(mod(x(:,1),l))<0.5) && (min(mod(x(:,2),l))>0.5)
Xr(s,k,w) = mod(x(end,1),l);
Yr(s,k,w) = mod(x(end,2),l);
else
Xb(s,k,w) = mod(x(end,1),l);
Yb(s,k,w) = mod(x(end,2),l);
end
% fig(1)
% plot(mod(x(end,1),l),mod(x(end,2),l),c);
% hold on
end
end
end
%hold off
fig(2)
plot(Xb(:),Yb(:),'b.')
%toc
  2 Comments
David Goodmanson
David Goodmanson on 12 Mar 2021
Hi Ahmed
You have three nested for loops with indices k,s,w, so for each occurrance in the for loops, you can save the X and Y data as 3 dimensional arrays with indices k,s,w. There are separate arrays for red and blue (does red occur?)
After all the calculations are done, for plotting purposes the 3d arrays won't work. The expression Xb(:) reads out, in a particular order, the 3d array into one long column of data. Yb(:) also reads out into a column, of course in the same order, so the Xb and Yb values match up. With those two columns you can make an xy plot that matches the plot-every-time procedure.
Preallocation of the 3d arrays occurs up toward the top.

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