Pursuer Evader Problem

There are several different mathematical models in diffy-ques and control theory that go under the category Pursuer/Evader (depending on the type of Evader movement and Pursuer predict models -- plus the classic "go pointing where he is"), so it would be important to know which one you want. As well, 2D, 3D, or nD? Some of the classics have exact solutions or have functional solutions in terms of hypergeometrics, so do you want an incremental simulation based on the move rules (like a step based solution of the diffy-que) or a more robust that just puts the proper parameters into the solution functions (less error)?