PSE for ODEs
EpODE (ExPert system for Ordinary Differential Equations)
is a problem-solving environment (PSE) that provides the computational facilities necessary to
find a numerical solution of the IVP of ODEs.
The main thrust of EpODE is its automated identification of problem
properties and method properties. The first version of EpODE was designed
especially for the numerical solution of ordinary differential equations of
stiff type (many software packages can not integrate such equations).
EpODE is independent from any other computer application.
Moreover, in EpODE, no supplementary code will be generated when a
new method will be added.
Two advantages of using EpODE must be underlined:
- We consider that a fixed database of numerical methods is not quite a very
good solution. There are many problems which can be solved easily using some
methods which are problem dependent (for example, using some exponential fitting
procedure). The user must have the possibility to test itself a
particular method which seems to be adequate for his problem and thereafter to
compare the results with those of the "expert".
- On another hand, solving IVP with a large equation number implies a
extremely large run-time. A possible solution consists in the use of the
computer network to which, in most cases, the EpODE host computer is connected.
In the case of a large number of equations EpODE uses numerical
codes combined with PVM procedures in the
idea to distribute the computations on some processors of a local network.
The PVM package have been chosen to support the processes creation
and intercommunications since it comes into general use on many different operating systems.