An ε-Uniform Initial Value Technique For Convection-Diffusion Singularly Perturbed Problems

In this paper, we have proposed an ε-uniform initial value technique for singularly perturbed convection-diffusion problems in which an asymptotic expansion approximation of the solution of boundary value problem is constructed using the basic idea of WKB method. In this computational technique, the original problem reduces to combination of an initial value problem and a terminal value problem. The initial value problem happened to be singularly perturbed problem, which is then solved by using a hybrid scheme on an appropriate piecewise uniform Shishkin mesh, whereas trapezoidal scheme is applied to terminal boundary value problems. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples.