Error estimates for a class of partial functional differential equation with small dissipation

摘要

This article deals with a class of partial functional differential equation with a small dissipating parameter on a rectangular domain. Classical numerical methods for solving this type of problems reveal disappointing behavior or are tremendously expensive in computer memory and processor time. This arises because the precision of an approximate solution depends inversely on perturbation parameter values and, thus, it deteriorates as a parameter decreases. Therefore, it is of particular interest to develop numerical methods whose error estimates would be independent of the perturbation parameter contaminating the solution. In order to overcome the said difficulty we derive robust parameter uniform error estimates for a class of partial functional differential equations. The analysis presented in this paper uses a suitable decomposition of the error into smooth and a singular component combined with the appropriate barrier functions and comparison principle.