Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points

Abstract

In this thesis, we aim to study finite volume approximations which approximate the solutions of convection-dominated problems possessing the so-called interior transition layers. The stiffness of such problems is due to a small parameter multiplied to the highest order derivative which introduces various transition layers at the boundaries and at the interior points where certain compatibility conditions do not meet. Here, we are interested in resolving interior transition layers at turning points. Depending on the characteristics, the latters are identified as turning point layers or characteristic interior layers. The proposed semi-analytic method features interior layer correctors which are obtained from singular perturbation analysis near the turning points. We demonstrate this method is efficient, stable and is of 2nd-order convergence in the approximations.