A Computer Algebra Approach for Solving Singularly Perturbed Initial Value Problems

Singular perturbation problems, also known as stii, are not easily treated analytically or numerically, as the partition of the system on slow and fast subsystems in the vicinity of the singular point(s) is required. The most common analytical technique to study such problems is the method of matched asymptotic expansions which involves nding outer and inner solutions of the system and their matching. While this method is widely used in many areas, there is no general implementation of it in computer algebra. This paper discusses a computer algebra implementation (in Maple of the formal algorithm proposed by Nipp 9 for solving singularly perturbed initial value problems. A precise choice of scalings for an appropriate sequence of approximating systems is motivated by introducing a correspondence between a system of ordinary diierential equations containing a small parameter and a convex polyhedron.