B-spline method for a class of singular two-point boundary value problems using optimal grid

摘要

In this paper, we present B-spline method for solving singular two-point boundary value problems for a certain differential equation having singular coefficients. The given singular boundary value problem is modified at the point of singularity. The modified problem is then solved by B-spline. In the case of non-linear problems, we first linearize the equation using Quasilinearization technique and the resulting problem is solved by B-spline. Error estimates are obtained which enable a deferred correction to be made. Optimal grid has been generated using the method. Some numerical examples have been included to demonstrate the efficiency of the method.