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In most of the books I've seen, the authors explain various methods for solving partial differential equations, sometimes give recommendations about usage and limitations of the approach, but I never seen a complete algorithm or a guide how to choose an appropriate method. For example

  1. Determine type of you PDE (type, order, linear/nonlinear etc)
  2. If the PDE is linear, try method one.
  3. If not, but the coefficients satisfy the conditions, try method two.

I would expected such a guide in various "PDE for engineers" books, but they do not have it. It would be also nice to have a summary or roadmap for pros and con of the different methods. Could anybody suggest such a book?

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Do you know any book that does the same for ODE? –  timur May 30 '12 at 11:41
    
@timur no, but it might be interesting for me as well –  zeliboba May 30 '12 at 12:23
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A complete algorithm is probably too much to ask for, but you might be interested in "Handbook of Differential Equations" by Daniel Zwillinger. –  Hans Lundmark May 30 '12 at 17:27
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Let us forget about ODEs. How about a human-exectuable general algorithm for finding an integral? –  timur May 31 '12 at 0:48
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Also, there are three major branches of "solving" PDEs. (a) Analytical: which cares about existence and uniqueness of solutions, and their dependence on boundary or initial data (b) Algebraic: which studies the symmetries and conservation laws of an equation, and methods of producing exact solutions (c) Numerical: which involves the analysis of discretisation methods, computational algorithms, their efficiency, their convergence, and their errors, as well as the application of those algorithms to provide numerical solutions. Are you specifically interested in one of the three branches? –  Willie Wong Jun 1 '12 at 8:23
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A complete algorithm is probably too much to ask for, but you might be interested in "Handbook of Differential Equations" by Daniel Zwillinger. (Google Books link.)

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it also has a (rather expensive) CD-ROM version amazon.com/exec/obidos/ASIN/0127843965/zwillingerhomepa (just for a reference) –  zeliboba Jun 3 '12 at 18:06
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