Abstract:
In this thesis, higher-order layer resolving numerical scheme is presented for singularly
perturbed boundary turning point problems. The method is attempted on piecewise uniform
mesh of the shishkin mesh type. The discrete problem is transformed in to linear systems of
algebraic equations. That can be solved using Thomas algorithm. To validate the applicability
of the proposed method, some model examples have been considered and solved for different
values of perturbation parameter and mesh sizes. Both the theoretical investigation and
numerical illustration have been confirmed for the method. As it can be observed from the
numerical results presented in tables and graphs, the present method approximate the exact
solution very well. Moreover, the present method give better results than some existing
numerical methods reported in the literature.
