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My question is whether one's code must always contain the actual description of spatial discretization written explicitly or whether the Method of Lines can be called as an internal routine. If so how could I implement such a black-box approach to solve this problem? Still, is this approach always enough or explicit discretization is sometimes unavoidable?

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    The option Method -> "MethodOfLines" calls the method of lines internal routine. In the linked problem, NDSolve complains about the boundary conditions; in the currently accepted answer such a check by NDSolve is bypassed. I added my own answer to the linked question to show how to use the internal method. Probably this question should be closed as a duplicate. – Michael E2 Nov 30 '18 at 02:15
  • Probably yes. But have you seen any question or tutorial about the limitations of using the method of lines as an internal routine? Should anyone bother to learn how to include spatial discretization explicitly in ones code? Or it would be just a loss of time? –  Nov 30 '18 at 11:53
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    The Method of Lines tutorial and the FEM tutorial both discuss spatial discretization with the method of lines. There are questions on this site about particular issues a user is having with the spatial discretization of their PDE. – Michael E2 Nov 30 '18 at 12:36
  • Thanks and sorry for duplicating. –  Nov 30 '18 at 18:55
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    It's not problem. There is an unresolved question concerning your linked question: Can the original setup be solved as DAE using the method of lines (without differentiating the xt[] equation? That might be added as an answer to that question, too. I haven't had time to investigate it though. – Michael E2 Nov 30 '18 at 19:21

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