Discrete format for a class of wave systems

This study aims to explore a class of computational solutions to semilinear hyperbolic equations. The nonlinear terms in the equation, including the dissipation term and the external source term, make the nonlinear characteristics of the equation more complex. Nevertheless, the influence of these nonlinear features on discretization is still significant and cannot be ignored. Therefore, this study concentrates on how to construct an effective discretization method to ensure the accuracy of nonlinear terms in discrete formats. According to this, two kinds of effective schemes are designed by using the idea of transforming nonlinearity into linearity and iteration theory, they are finite difference scheme and multiple integral finite volume scheme respectively. And then we gave numerical examples for the above two schemes. Comparing with the existing reliable numerical results, it is demonstrated that these formats are effective and feasible.