A fitted numerical method for a class of singularly perturbed convection delayed dominated diffusion equation
Abstract
A new exponentially fitted numerical method based on uniform mesh is proposed to obtain
the solution of a class of singularly perturbed convection delayed dominated diffusion
equation. The considered equation is first reduced to the ordinary singularly perturbed
problem by expanding the term containing negative shift using Taylor series expansion
procedure and then a three-term scheme is obtained using the theory of finite differences. A
fitting factor is introduced in the derived scheme with the help of singular perturbation
theory. Thomas algorithm is employed to find the solution of the resulting tridiagonal system
of equations. Stability and convergence of the proposed method are discussed. The method
is shown to be first accurate. Computational results for two example problems are presented
for different values of the grid point, N and perturbation parameter, . It is observed that
the method is capable of approximating the solution very well.