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.

在本文中，我们推荐了一种新颖的高精度紧凑型三级隐式数值方法，时间二阶和空间四阶，使用不等网格求解无理域上的 3D 拟线性双曲方程。讨论了不等网格Telegraphic方程模型的稳定性分析，表明所提出的Telegraphic方程方法是无条件稳定的。算子分裂技术用于求解 3D 线性模型方程。在这项技术中，我们使用非常著名的三对角求解器技术来求解无理域上的一组三对角矩阵。该方案在无理域上的大量物理问题上进行了检验，以证明该方案的准确性和效率。