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

Question

Thomas Veith 2019-5-30

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/464836-how-can-i-solve-this-ode-1000-times-with-random-variables

评论： Star Strider 2019-5-30

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?

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Thomas Veith 2019-5-30

在 MATLAB Online 中打开

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);

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Answer 1

Star Strider 2019-5-30

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/464836-how-can-i-solve-this-ode-1000-times-with-random-variables#answer_377261

在 MATLAB Online 中打开

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.