Solving autonomous linear systems of differential/difference equations

[jozko.slaninka]

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.

 

[Mandelbroth]

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.

I've found, after cursory inspection...

• "On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations" by T. S. Rybnikova
• "Solution of an Infinite System of Differential Equations of the Analytic Type" by F. R. Moulton
• http://www.jstor.org/discover/10.2307/1989496?uid=3739840&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=21102191980473 by William T. Reid
• Stack Exchange is typically my second stop for math research after Wikipedia.
• Or, of course, you could just go ask the magic fairies of internet land.

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.

 

[jozko.slaninka]

I've found, after cursory inspection...

• "On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations" by T. S. Rybnikova
• "Solution of an Infinite System of Differential Equations of the Analytic Type" by F. R. Moulton
• http://www.jstor.org/discover/10.2307/1989496?uid=3739840&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=21102191980473 by William T. Reid
• Stack Exchange is typically my second stop for math research after Wikipedia.
• Or, of course, you could just go ask the magic fairies of internet land.

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.

Thanks a lot!

 

[Mandelbroth]

Thanks a lot!

You're most certainly welcome. Math is interesting!