The alternating direction implicit difference scheme and extrapolation method for a class of three dimensional hyperbolic equations with constant coefficients

This paper conducts a study on the alternating direction implicit (ADI) difference schemes for a class of three dimensional hyperbolic equations with constant coefficients. The central difference methods are employed in the temporal and spatial direction. The solvability, stability, and convergence of the proposed ADI schemes are proven. Moreover, the Richardson extrapolation method is established to enhance the accuracy of the algorithm. Numerical examples are presented for the errors and convergence orders of the established ADI schemes and extrapolation schemes. By comparing the results of numerical examples, it can be concluded that the proposed Richardson extrapolation method can effectively improve the accuracy of the numerical solutions and reduce the errors.