Abstract
This paper focuses on the numerical algorithm of a class of semilinear hyperbolic equation. The dissipation term and external force source term existing in the equation enhance the nonlinearity of the model and make the nonlinear effect complicated. However, this nonlinear effect has a great influence on the discrete scheme, which cannot be neglected. Discretizing the nonlinear terms to ensure the validity of the scheme is the core issue in this paper. An effective scheme based on linearization techniques and iteration theory is proposed. It is based on the finite difference method. The efficiency of the proposed schemes was verified via some numerical examples showing that they compare well with existing methods.