Analytic Solution of Qualitative Differential Equations

Abstract

Numerical simulation, phase-space analysis, and analytic techmques are three methods used to solve quantitative differential equations. Most work in Qualitative Reasoning has dealt with analogs of the first two techniques, producing capabilities applicable to a wide range of systems. Although potentially of benefit, little has been done to provide closed-form, analytic solution techniques for qualitative differential equations (QDEs). This paper presents one such technique for the solution of a class of ordinary linear and nonlinear differential equations. The technique is capable of deriving closed-form descriptions of the qualitative temporal behavior represented by such equations. A language QFL for describing qualitative temporal behaviors is presented, and procedures and an implementation QDIFF that solves equations in this form are demonstrated.