How to make a matrix with one unknown variable, that can be in a for loop and can be used in ODE45

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Marlene Dehn 2019-3-21

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https://ww2.mathworks.cn/matlabcentral/answers/451361-how-to-make-a-matrix-with-one-unknown-variable-that-can-be-in-a-for-loop-and-can-be-used-in-ode45

评论： Walter Roberson 2019-3-21

Hi, at the moment I have the following code. I think the problem is the matrix B is a symbolic funtion, and not a anonymous function, but I can't make an anonymous function to work within a loop.

syms t x u
l=50;         
v = 50; 
N = 5;
for n = 1:N
    for c = 1:N
        B(n,c) = sin((n*pi*v*t)/l) * sin((c*pi*v*t)/l);
    end
end
T = [t,t,t,t,t];
Td = [diff(t,t) diff(t,t) diff(t,t) diff(t,t) diff(t,t)];
tspan=[1,0.1,10];
xinit=zeros(1,2*N+2);
z=[T u Td diff(u,t)]';
[t,z]=ode45(B*z,tspan,xinit);

It's my first time using the ode45, so I'm not sure I'm using that one correct either.

So now I'm trying the mathworks-community, so I really hope you guys can help!

回答（1 个）

Walter Roberson 2019-3-21

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https://ww2.mathworks.cn/matlabcentral/answers/451361-how-to-make-a-matrix-with-one-unknown-variable-that-can-be-in-a-for-loop-and-can-be-used-in-ode45#answer_366548

See the documentation for odeFunction . In particular, follow the flow of calls that is used in the first example.

Yeah, the thing is we need to find a N, that is good enough to erased the infinite summation, that is why we need the for loop from 1:N, so the N can be a number from 1-infinite. But when we have the solution, we can figure out what the N needs to be through a convergence-analysis.

Walter Roberson 2019-3-21

It is not at all obvious to me that you can justify a finite truncation. That would require that the Tn functions are decaying with increasing n, which is not an obvious conclusion. I can see that it might happen because of the increasing (n*pi/l)^4 multiplier in the first term could force the Tn smaller and smaller to match the right hand side, but the infinite summation makes things difficult.

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