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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?2012-05-30
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    @timur no, but it might be interesting for me as well2012-05-30
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    'I would expected such a guide in various "PDE for engineers" books, but they do not have it.' That is because such a general algorithms is not available for at least two reasons: (a) most PDEs do not admit nice closed-form solutions (b) there are a lot more PDEs than people have had studied to date.2012-05-30
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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.2012-05-30
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    Let us forget about ODEs. How about a human-exectuable general algorithm for finding an integral?2012-05-31
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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?2012-06-01
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    @WillieWong I do not restrict myself to particular branch, the final aim is to get a solution, but analytical solution is preferable where available. In fact, I do not need in-depth details behind every branch or method, just a summary when it is applicable, pros and cons, alternatives and references for further explanations and details.2012-06-03
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    @HansLundmark thank you, this book looks like the one I was looking for! From preface: "Eventually, I created a list of the different techniques that I knew. Each technique had a brief description of how the method was used and to what types of equations it applied. As I learned more techniques, they were added to the list. This book is a direct result of that list." Could you please make an answer instead of comment, so I can accept it?2012-06-03
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    @zeliboba: OK, done.2012-06-03

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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 http://www.amazon.com/exec/obidos/ASIN/0127843965/zwillingerhomepa (just for a reference)2012-06-03