We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling transformation, which is a variant of what was successfully used in the case of nonlinear parabolic equations. A careful study of the convergence of the proposed scheme is carried out and several numerical examples are performed in illustration.

翻译：我们发展了一种基于有限差分格式与重标度技术的混合方案，用于逼近非线性波动方程的解。为在数值上再现爆破现象，我们提出了一种尺度变换规则，该规则是成功应用于非线性抛物型方程情形下的一种变体。本文对所提格式的收敛性进行了细致研究，并通过多个数值示例加以说明。