Difference schemes for the singularly perturbed Sobolev periodic boundary problem

摘要

A finite-difference method is suggested and analyzed for evolution equations of Sobolev type in a single space variable and with boundary layers. The convergence and error estimates for an exponentially fitted difference scheme in an equidistant mesh are obtained. The numerical methods discussed here are extremely robust, in the sense that they have good convergence properties not only for small values of the perturbation parameter, but also for moderate and large values.