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
- Determine type of you PDE (type, order, linear/nonlinear etc)
- If the PDE is linear, try method one.
- 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?