Choosing an Algorithm

The problem as posed does not fit neatly into the categories defined in (1.1). By considering the accuracy and stability properties of the various algorithms described in these notes you have to decide which is the most appropriate algorithm to use for solving the problem. The computer time required by the algorithm as well as the ease with which it can be programmed may be legitimate considerations. It may not be possible to solve the the stability equations exactly in the most general case. Nevertheless you should be able to deduce enough information on which to base a decision (See (e.g.) section 1.7). In your report you should discuss the merits and demerits of the various possible algorithms and explain the rationale behind your choice. You should also write a program to implement your chosen algorithm and test it for various values of $\delta t$ and in all the physically significant regimes.