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I want to learn a numerical method for PDEs other than finite difference method. After some research on internet i have found Rothe method and it looks interesting to me. Unfortunately, i couldn't find a good book/ notes for starting. Can you suggest me a book to study? What is prerequisites/corequisites for the Rothe method?

Thanks in advance...

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    $\begingroup$ Rothe's method is semidiscretization in time before space (a transpose of the more common "method of lines"). That choice is orthogonal to the discretization scheme (finite difference/volume/element). I suggest reading about finite volume methods if you are interested in hyperbolic problems (wave propagation and similar) or finite elements if you are interested in elliptic or parabolic problems. $\endgroup$
    – Jed Brown
    Dec 4 '14 at 19:53
  • $\begingroup$ @Jed Brown first of all thanks for answering my question. Actually i dont understand the relation between rothe method and finite element method. Can you explain that relation much more ? i will be grateful if you could. $\endgroup$
    – math
    Dec 4 '14 at 20:12
  • $\begingroup$ FD is a space or time discretization. The distinction between Rothe vs Method of Lines is only whether you discretize in time-then-space or space-then-time. You said you want to go beyond FD, so read up on FV or FE. This is orthogonal to using Rothe vs Method of Lines. (I prefer MoL because I think it is much better at enabling software reuse.) $\endgroup$
    – Jed Brown
    Dec 4 '14 at 20:55
  • $\begingroup$ Related: scicomp.stackexchange.com/questions/2962/… $\endgroup$
    – Paul
    Dec 4 '14 at 21:00
  • $\begingroup$ Ok @Jed Brown thank you so much. can you suggest me a good introductory book for FEMs and a basic illustration of MoL $\endgroup$
    – math
    Dec 4 '14 at 21:18
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Here's a 30 minute introduction that explains the difference between the method of lines and the Rothe method: http://www.math.tamu.edu/~bangerth/videos.676.26.html

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