Solving Higher Order Dynamic Equations on Time Scales as First Order Systems

Time scales calculus seeks to unite two disparate worlds: that of differential, Newtonian calculus and the difference calculus. As such, in place of differential and difference equations, time scales calculus uses dynamic equations. Many theoretical results have been developed concerning solutions of dynamic equations. However, little work has been done in the arena of developing numerical methods for approximating these solutions. This thesis work takes a first step in obtaining numerical solutions of dynamic equations|a protocol for writing higher-order dynamic equations as systems of first-order equations. This process proves necessary in obtaining numerical solutions of differential equations since the Runge-Kutta method, the generally accepted, all-purpose method for solving initial value problems, requires that DEs first be written as first-order systems. Our results indicate that whether higher-order dynamic equations can be written as equivalent first-order systems depends on which combinations of which dynamic derivatives are present