High resolution numerical algorithm of order (2, 4, 4) for 2D quasi-linear hyperbolic equations based on half-step discretization on an unequal grid

Abstract

This study suggests a novel three-level implicit half-step scheme of order two and four in time and space direction respectively, utilizing an unequal grid for the approximation of 2D quasi-linear hyperbolic partial differential equations on an unequal grid. The stability analysis of the model Telegraphic equation for unequal grid has been discussed and it has been demonstrated that the presented method is unconditionally stable for the Telegraphic equation. The alternating direction implicit (ADI) techniques are discussed for linear difference equations on a dissimilar domain. The developed method investigated several well-known physical problems on an unequal mesh to demonstrate its accuracy and efficiency.