High resolution operator compact implicit half-step approximation for 3D quasi-linear hyperbolic equations and ADI method for 3D telegraphic equation on an irrational domain

Abstract

We propose a novel three-level implicit half-step method of order two in time and four in space using unequal mesh for the solution of three-space dimensional quasi-linear hyperbolic equations on an irrational domain. The proposed method is directly applicable to 3D hyperbolic equation with singular coefficients, which is the key charisma of our scheme and we do not need any fictitious points for computation. The stability analysis of the model problem for unequal mesh has been discussed and it has been shown that the proposed method for Telegraphic equation is unconditionally stable. Alternating direction implicit (ADI) method by the help of a tri-diagonal solver is used to solve 3D linear schemes in three sweeps. The proposed method is scrutinized on several physical problems on dissimilar domain to exhibit the accuracy and effectiveness of the proposed method.