Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasilinear hyperbolic equations (Q2762699)

\textit{R. K. Mohanty, M. K. Jain}, and \textit{K. George} [J. Comput. Appl. Math. 70, No. 2, 231-243 (1996; Zbl 0856.65098)] presented a fourth-order finite difference solution for a two space dimensional nonlinear hyperbolic equation. Further \textit{R. K. Mohanty} and \textit{P. K. Pandry} [Int. J. Comput. Math. 68, No. 3-4, 363-380 (1998; Zbl 0911.65097)] discussed a fourth-order approximation at the first time level for the numerical solution of a one space dimensional hyperbolic equation. In this paper the authors extend the strategy for solving a two space dimensional quasilinear hyperbolic equation. An operator splitting method for a linear hyperbolic equation having a time derivative term is proposed and a linear stability analysis is discussed. Two numerical results are presented.