A Padé–Legendre Reconstruction Approach in Capturing Shock Behaviour

Many numerical methods for solving partial differential equations having shock behaviour produce unphysical oscillations. This study aims to prove the efficiency of applying Padé-Legendre reconstruction technique for stabilization of these oscillations. To get better, physically acceptable solutions of the advection dominated Burgers equation, the fourth-order finite difference method (FD4) and the Padé-Legendre reconstruction technique (PLR) are combined. The PLR is designed for the stabilization process of discrete solutions produced by the FD4 with the use of suitable composite numerical integrations. It has been proved that the present approach can capture shock behaviours as well as minimize the maximum errors produced by FD4. Two challenging test problems having shock behaviours are considered, and the positive effect of the PLR is illustrated.