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.