A Shishkin mesh for a singularly perturbed Riccati equation

摘要

In this paper a singularly perturbed Riccati initial value problem is examined. Parameter explicit bounds on the solution and its derivatives are given. A numerical method composed of an implicit difference operator and a piecewise-uniform Shishkin mesh is constructed. A theoretical parameter independently bound on the errors in the numerical approximations is established. Numerical results are presented which are in agreement with the theoretical error bound.