Declaring an anonymous function for solving an odes system

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gringer45 2015-9-29

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评论： Walter Roberson 2015-9-29

Hi there,

I am trying to integrate a system of ODES, I am being partially successful defining the function in another file, but when trying to do that using an anonymus function, it is not working, I am not sure what is wrong.

So, the working version is:

in F.m file:

function x = F(t,theta)
    N = 10; lambda = 1; k = 4;
    omega = lambda*tan(pi*(rand(1,N)-0.5));
    x = omega' + k/N*sum(sin(repmat(theta,[1 N])' - repmat(theta,[1 N])),2);

and then:

N = 10;
[t,x] = ode45(@F,[0,10],ones(N,1));

And the one Im trying to make work is:

N = 10; lambda = 1; k = 4;
omega = lambda*tan(pi*(rand(1,N)-0.5));
FK = @(t,theta)   omega' + k/N*sum(sin(repmat(theta,[1 N])' - repmat(theta,[1 N])),2) ;
[t,x] = ode45(FK,[0,10],ones(N,1));

Thanks in advance

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Adam 2015-9-29

What do you mean by 'not working'? Is there an error message or are you just getting incorrect results?

gringer45 2015-9-29

Incorrect results, totally different to the results I get with the other method. No matlab errors though.

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Answer 1

gringer45 2015-9-29

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Ok, I just figuered it out.

The omega function was being defined only once in the second case, so it was being used the same for each run instead of a new one.

FK = @(t,theta)   lambda*tan(pi*(rand(N,1)-0.5)) + k/N*sum(sin(repmat(theta,[1 N])' - repmat(theta,[1 N])),2) ;

instead of

omega = lambda*tan(pi*(rand(1,N)-0.5));
FK = @(t,theta)   omega' + k/N*sum(sin(repmat(theta,[1 N])' - repmat(theta,[1 N])),2) ;

cheers

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Walter Roberson 2015-9-29

No, the other way around. When you use rand() or randn() in your ODE function, you make the function discontinuous and non-repeatable. This would drive the integrator to smaller and smaller step sizes unless you are using a fixed-step solver. If you must have randomness, you should define the random contributions ahead of time, possibly with some method of interpolating at interior times.

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