Help With ODEs Solver(ode45)

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?

Answer 1

[David Goodmanson]

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

[Ahmed Sulaiman Ahmed Al Rawahi]

Hello David.

I appriecate your help! That is much faster and gave me a better results.

If you have time, would you mind walking me through the changes you made and brefly explain what you did ?

Thank you again.

[David Goodmanson]

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.