ABSTRACT
In the present work, a boundary value problem for one type of singularly perturbed differential-difference equations (SPDDEs) is considered. To find an approximate solution for this type of problem, we have used an exponential B -spline collocation method. The method is shown to be of a second-order convergent. We have employed the proposed scheme on three numerical examples and compared the result with previously published schemes, and it is found that our results are better than the results reported in the literature. Some recent work reported to solve the SPDDEs is also reviewed. The behavior of the approximated solution is presented in graphs for all the considered problems. From the results, it can be concluded that the discussed method of the exponential B -spline is capable of obtaining results of the required accuracy.
