Method selection

The actual version of EpODE expert is based on a method database represented by the (text) files in which the classical methods were saved and which are stored in the subdirectory 'Methods' from the EpODE directory (any modification of this file or the position of this files relative to the parent directory can conduct to some errors). The methods are divided in four categories: In each such subclass the methods are arranged in increasing order of accuracy, and, for the same order of accuracy, in increasing order of constant error. No list of methods will be selected until a problem will be defined. Depending on the problem properties (in this implementation, depending on the stiff-classification) and on the user option for sequential or concurrent computations, a subclass of methods will be selected (i.e. the method list will appear on the right panel of EpODE).

The expert-function is constructed as follows. After the list of available methods for the given problem has been established, the first method from the list is selected, loaded and tested, i.e. the computation time is estimated and compared with the maximum admitted level, and, also, a test of the availability of the necessary storage space is performed. If these tests are positive, the computation process starts (the process evolution is the same as in the case of the human-expert mode; the only difference is that the expert-program informs the user about the evolution of the computation process, i.e. more messages will appear than in the case of the human-expert mode); otherwise the next method is selected from the list, loaded and tested. If no other method follows the current one in the list, the maximum computation time is incremented, and the first method of the list is again selected, loaded and tested. If the maximum computation time has reached to an maximum limit, then the maximum admitted error level is increased (also until a reasonable superior limit). Numerical tests on some known problems have been shown that cycle can conduct to a approximate solution.

The methods which were selected to be part of the method database are some well-known methods, which were tested by many researchers in ODEs. The user can also test its own methods adding these methods to the expert (as described in the paragraph about the human-expert mode).

The next version of EpODE will include a more elaborated expert which we hope to be implemented in Clips.

Example for the system B1.