This article deals with hyperbolic partial differential equations with piecewise constant arguments and variable coefficients. This study, therefore, with the aid of the finite difference technique, aims at presenting a numerical solution scheme for solving such types of equations. The stability, consistency, convergence, and convergence rate of our proposed numerical method are investigated. Moreover, the process of the computation of the analytical solution is studied. In order to support and confirm our theoretical results, some numerical examples are also presented. The figures of the numerical and analytical solutions and also the tables of errors are provided to demonstrate the validity of our proposed scheme.

本文讨论具有分段常数参数和可变系数的双曲型偏微分方程。因此，本研究将借助于有限差分技术，提出一种用于求解这类方程式的数值求解方案。研究了我们提出的数值方法的稳定性，一致性，收敛性和收敛速度。此外，还研究了解析解的计算过程。为了支持和证实我们的理论结果，还提供了一些数值示例。数值和解析解的图以及误差表被提供来证明我们提出的方案的有效性。