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I have a simple ODE to solve of matrix.

$\frac{dM}{dt} = \alpha J$

where $M$ and $J$ are matrices. How can I proceed to solve them?

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  • $\begingroup$ So $J$ depends only on time? $\endgroup$ Mar 30, 2017 at 6:43
  • $\begingroup$ For the isolated equation above, J only depends on time. $\endgroup$
    – jkhadka
    Mar 30, 2017 at 6:56

1 Answer 1

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Just integrate, i.e. \begin{align} M(t)_{i,j} = (M_0)_{ij}+\alpha\int^t_{t_0}J(s)_{ij}\ ds. \end{align}

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  • $\begingroup$ ... This "entrywise" (exact) answer means that the matrix structure of your problem is unimportant.... $\endgroup$
    – Jean Marie
    Mar 30, 2017 at 6:52
  • $\begingroup$ hey, my main confusion was if the element wise solution can be used. It means each element grow independently and thus, I was concerned if it is fine. Is there any literature I can study on this? $\endgroup$
    – jkhadka
    Mar 30, 2017 at 6:55

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