Anatomy of AGNES: an automatic generator of numerical equation solutions

An expert system has been designed and constructed which can accept a symbolic description of a mathematical model in terms of partial or ordinary differential equations along with boundary, initial, and subsidiary conditions and automatically generate and execute programs for their numerical solution. Classes of differential equations and numerical solution methodology are realized in terms of an object oriented representation embedded in a logic programming environment. AGNES solves the model equations by parsing the input equations, classifying them, and choosing an appropriate numerical solution method. Once a numerical method is chosen, an internal form of the algorithm is generated from an object oriented representation of numerical solution methods. A translator then transforms the algorithm into a program in a specific language (currently C) for execution.