On the Nipp polyhedron algorithm for solving singular perturbation problems

This paper deals with a constructive approach for finding local approximations to singular perturbation problems. This approach is based on Nipp polyhedron algorithm wherein a correspondence between a singularly perturbed system and a convex polyhedron is established. The task of finding local approximations reduces to the linear programming problem of finding vertices of polyhedron adjacent to the zero vertex. The paper presents Nipp polyhedron algorithm and considers its computer implementation in Maple. Two non-trivial examples are given.