Detection and Integration of Oscillatory Differential Equations with Initial Stepsize, Order and Method Selection

摘要

Within any general class of problems there typically exist subclasses possessed of characteristics that can be exploited to create techniques more efficient than general methods applied to these subclasses. Two such subclasses of initial-value problems in ordinary differential equations are stiff and oscillatory problems. Indeed, the subclass of oscillatory problems can be further refined into stiff and nonstiff oscillatory problems. This refinement is discussed in detail. The problem of developing a method of detection for nonstiff and stiff oscillatory behavior in initial-value problems is addressed. For this method of detection a control structure is proposed upon which a production code could be based. An experimental code using this control structure is described, and results of numerical tests are presented. 3 figures. (ERA citation 06:017895)