Symbolische Lösung von Differentialgleichungen 1. Ordnung und 1. Grades Durch Heuristische Programmierung

Abstract

The problem of solving first order, first degree differential equations symbolically is characterized as a heuristic search process. An investigation into the problem of automatically solving such differential equations has resulted in a heuristic program, called EULE. The selection and the realization of the methods for EULE are based on a detailed analysis of the problem domain: the standard work of Kamke (1961), which is representative of the state of the knowledge of differential equations, was examined in three different respects: the collected methods of solution, the methods utilized for the collection of differential equations and the structure of these differential equations. The realization of the methods is based on this result and on defined principles which ensure the effectiveness of the program. The effectiveness of EULE can be characterized by the fact that EULE achieved a ‘rate of solution’ of 90% for Kamke’s representative collection of first order, first degree differential equations and a rate of 95% for Murphy’s (1960) representative collection. For two collections for training students EULE achieved a rate of 100%.