Numerical study of a few special classes of generalized viscous problem

Abstract

This thesis deals with the numerical treatment of various viscous problems that are dictated by a parameter; in particular, singularly perturbed dierential equations.The main focus is on the two special classes of viscous problems: a convection diusion problem which lacks regularity in the coecient present in the dierential equation and a turning point problem with smoothly varying coecients.It is known that solutions of these problems has dierent kinds of layers and annewlineappropriate discretization is needed to resolve such layers. In line with this, we design and analyze a new a priori mesh(referred to as G-mesh) adapted to the layer behavior of the solution and employ upwind numerical scheme on the proposed mesh. Further, we investigate the performance of the proposed G-mesh and robustness of the numerical method. The eciency is conrmed by a comparison with a few other meshes such as Shishkin, harmonic and B-type meshes.