A Mathematica Solver for Two-Point Singularly-Perturbed Boundary Value Problems

This paper introduces a Mathematica solver which constructs approximate symbolic solutions of second-order singularly-perturbed boundary value problems. The employed symbolic technique is based on the method of matched asymptotic expansion and the Nipp polyhedron algorithm for finding appropriate scalings in local approximating systems. The main command BVPSolve uses the standard Mathematica syntax of the Solve-type commands. The package finds approximate solutions of second-order linear, quasilinear and semilinear singularly perturbed boundary value problems. Several illustrative examples are shown. The package can be used in research and teaching. It can also be used for initialising numerical solvers for boundary-value problems.