High precision implicit method for 3D quasilinear hyperbolic equations on a dissimilar domain: Application to 3D telegraphic equation

Abstract

In this paper, we recommend a novel high accuracy compact three-level implicit numerical method of order two in time and four in space using unequal mesh for the solution of 3D quasi-linear hyperbolic equations on an irrational domain. The stability analysis of the model Telegraphic equation for unequal mesh has been discussed and it has been shown that the proposed method for Telegraphic equation is unconditionally stable. Operator splitting technique is used to solve 3D linear model equations. In this technique, we use very well-known tri-diagonal solver technique to solve a set of tri-diagonal matrices on an irrational domain. The projected scheme is examined on numerous physical problems on irrational domain to demonstrate the accurateness and efficiency of the suggested scheme.