How can I solve this ODE 1000 times with random variables?

So I have this code:

tspan=[1 7];A0=rand;P0=rand;g=rand;p=rand;B=rand;
[t,x] = ode45(@(t,x) [-g*x(1) + p*x(1); -x(1)*x(2)+ B*x(2)], tspan, [A0 P0])

And it works perfectly.

But what I want to do is run it 1000 times and change the random inputs each time, and generate new solutions every time. I've tried using the following:

n = 1000;
result = zeros(n,1);
for k=1:n
    tspan=[1 7];A0=rand;P0=rand;g=rand;p=rand;B=rand;
    [t,x(n)] = ode45(@(t,x) [-g*x(n(1)) + p*x(n(1)); -x(n(1))*x(n(2))+ B*x(n(2))], tspan, [A0 P0])
    result(k) = x(n);
end

But I get the error

Index exceeds the number of array elements (2).

Error in @(t,x)[-g*x(n(1))+p*x(n(1));-x(n(1))*x(n(2))+B*x(n(2))]

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Any advice?

[Thomas Veith]

Alternatively, if I try this:

n = 1000;
result = zeros(n,1);
for k=1:n
    tspan=[1 7];A0=rand(n);P0=rand(n);g=rand(n);p=rand(n);B=rand(n);
[t,x] = ode45(@(t,x) [-g*x(1) + p*x(1); -x(1)*x(2)+ B*x(2)], tspan, [A0 P0])
    result(k) = x(n);
end

I get the following error:

Error using odearguments (line 93)
@(T,X)[-G*X(1)+P*X(1);-X(1)*X(2)+B*X(2)] must return a column vector.

Error in ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Answer 1

[Star Strider]

You coded your differential equation correctly. Your ‘x’ variable has only two elements, so you cannot use ‘n’ (or ‘k’) to subscript them.

See if this does what you want:

n = 1000;
result = cell(n,1);
for k=1:n
    tspan=[1 7];A0=rand;P0=rand;g=rand;p=rand;B=rand;
    [t,x] = ode45(@(t,x) [-g*x(1) + p*x(1); -x(1)*x(2)+ B*x(2)], tspan, [A0 P0]);
    result{k} = x;
end

Note that because the time vector can change between your ode45 calls, a cell array is most appropriate. If you want a specific number of values to be returned each iteration, define ‘tspan’ as a vector of more than two elements.

[Thomas Veith]

That's perfect, thank you!

[Star Strider]

As always, my pleasure!

You might also want to store your parameters, so you know what the solution used.