turkmath.org

A differential equation is called singularly perturbed if it has a small parameter ε at the derivative of the highest order. Such equations often arise in applications, including flows with high Reynold numbers, flows in porous media, elasticity, as well as in other problems of mathematical physics. It is well known that the solution of such equations can contain boundary layers, and this causes various complications in the numerical treatment of the equations mentioned. For example, for small ε the method under consideration can be unstable or, on the other hand, it does not converge uniformly with respect to this parameter. Therefore, one has to develop approximation methods whose stability and convergence do not depend on ε.