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Solving autonomous linear systems of differential/difference equations

  1. Jul 28, 2013 #1
    I would like to ask if anybody knows something about the methods of solving infinite linear autonomous systems of first-order differential (or possibly difference) equations.

    There is a well-known method for solving finite-dimensional systems based on the computation of eigenvalues of the system matrix. I wonder if something similar can be done also for infinite-dimensional systems. Perhaps there is a method based on spectral theory...

    I am mainly looking for references to literature. I have found a reference to a Russian book:

    K.G. Valeev, O.A. Zhautykov, "Infinite systems of differential equations". (this is an English translation of the title)

    However, I am quite unable to find this book in local libraries, nor to find out what matters are dealt with in it. If anyone knows this book, I would be grateful for any alternative references dealing with similar matters. As well as for any other references.
  2. jcsd
  3. Jul 30, 2013 #2
    I've found, after cursory inspection...

    The book Numerical-Analytical Methods in the Theory of Boundary-Value Problems by N. Nikolai Iosifovich Ronto and A. Anatolii Mikhailovich Samoilenko references K.G. Valeev and O.A. Zhautykov's work on infinite systems. That may be a good stop if you can't find their book firsthand.
  4. Jul 31, 2013 #3
    Thanks a lot!
  5. Jul 31, 2013 #4
    You're most certainly welcome. Math is interesting! :biggrin:
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