Learn the Method of Lines: Textbook Resources for Industrial Problem Solving

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Can anybody suggest good resources for me to learn about the method of lines? I have budget to buy textbooks.

The boss has received a "request for proposal" from a client with deep pockets. That means they want us to submit a bid for a contract.

The client wants us to apply the method of lines to solving a standard category of numerical problems in our industry. Ordinarily this kind of problem is solved using a variety of simplification assumptions. It would seem that somebody has noticed that computers have gotten faster in the last 20 years, so we should be able to do better.
 
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try googling "method of lines" tutorial (note that only "method of lines" is quoted)

Or, post this in one of the math forums.
 
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