Abstract:
In this thesis, an exponentially fitted modified upwind difference scheme is presented for
solving singularly perturbed convection-diffusion two point boundary value problems whose
solution exhibits right boundary layer. A fitting factor is introduced in a modified upwind
scheme and is obtained from the theory of singular perturbations. Then, fitted modified upwind scheme is developed and a three term recurrence relation is obtained. A tri-diagonal
finite difference scheme is obtained and is solved by using the Thomas algorithm. To validate
the applicability of the proposed method two model examples have been considered and solved
for different values of perturbation parameters ε and mesh size h. Both theoretical stability
and numerical first order of convergence have been established for the method. The numerical
results have been presented in tables, graphs and further to examine the effect of fitted parameter on right boundary layer of the solution and oscillatory behavior of the solution. Several
linear and nonlinear problems are solved and observed, which show the presented method approximates the exact solutions very well. Concisely,
