How to preserve 2-d initial conditions after passing it into ode45?

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savitha muthanna
savitha muthanna 2021-4-19
评论： savitha muthanna 2021-4-20
Hi,
I pass 2d initial conditions, but ode45 linearizes it and makes the matrix into a 1-d array. How do I ensure it is handled as a 2-d array?
I have the following:
--------------------------------------
N=60;
x(1:N, 1:2*N) = 0; x(20,20)=1;
options = odeset('RelTol',1e-7);
[t1 y] = ode45('fputest1', [0:L:t], x, options, N);
-----------------------------------------------------
x is a 60x120 matrix. When I step through the code in ode45, x is a 7200 x 1, 1-d array. How do I ensure x remains a 2-d matrix? Also what are the dimensions of y, when the solver has finished? Is it 2-d if x is an array? What is it in the case x is a 2-d matrix?

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Walter Roberson
Walter Roberson 2021-4-19
When I step through the code in ode45, x is a 7200 x 1, 1-d array. How do I ensure x remains a 2-d matrix?
To do that, write your own version of ode45. The Mathworks version will always pass in the boundary conditions as a column vector.
Most people deal with the situation by simply reshape() the input almost immediately.
Also what are the dimensions of y, when the solver has finished?
y will be length(t1) by numel(x).
Your function is required to return a column vector that is numel(x) by 1, and integrated versions of that column will become rows of the output.
What is it in the case x is a 2-d matrix
Then y will be length(t1) by numel(x).
You can reshape y afterwards, such as
yperm = permute(reshape(y, length(t1), size(x,1), size(x,2)),[2 3 1]);
and now yperm(:,:,iteration) will be the 2D results at time t1(iteration)
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Walter Roberson
Walter Roberson 2021-4-20
for i = 1 : size(yperm,3)
surf(yperm(:,:,i), 'edgecolor', 'none');
pause(1);
end
or
volumeViewer(yperm)

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