The Method of lines

References: Malek-Madani: AEM with and , Addison Wesley, 7.18 project E pp. 511-515.

``Semi-numerical method''. Principle: replace space derivative by FD, leave time derivatives as they are. Thus reduce a PDE into a (large) system of ODE's.

Apply this technique to the heat equation.

• Explain the basic idea and implementation of the method
• Experiment and explain the -code on p. 513. Make suitable modifications
• Look at problems 1-6 on pp. 514-515. Pick at least 3-4 most interesting ones (probably it would not be a big job to cover even all of them). In addition or (partly) alternatively you can take some standard separation of variables heat-problems and study the error behaviour as the size of the system varies.