Abstract:
A fitted-stable central difference method is presented for solving singularly perturbed
two point boundary value problems with the boundary layer at one end (left or right) of
the interval. A fitting factor is introduced in second order stable central difference
scheme (SCD Method) and its value is obtained using the theory of singular
perturbations. Thomas Algorithm (also known as Discrete Invariant Imbedding
Algorithm) is used to solve the resulting tri-diagonal system. To validate the applicability
of the method, some linear and non-linear examples have been solved for different
values of the perturbation parameter. The numerical results are tabulated and compared
with exact solutions. The error bound and convergence of the proposed method has also
been established. From the results, it is observed that the present method approximates
the exact solution very well.
