In this article, a mixed element algorithm is presented to look for the numerical solution for a class of nonlinear wave model with the Caputo fractional derivative. By introducing two auxiliary functions and reducing order technique of fractional derivative, the studied model with high-order derivative in time is transformed into a coupled system including three lower order equations. Next, a fully discrete mixed element algorithm is formulated, where the temporal direction is approximated by a second-order scheme. The stability analysis of the proposed mixed scheme is done and optimal error estimates for three functions are derived. Finally, the numerical tests are carried out to verify the theory results.

在本文中，提出了一种混合元素算法来寻找一类具有Caputo分数阶导数的非线性波动模型的数值解。通过引入两个辅助函数和分数阶导数的降阶技术，将具有高阶导数的研究模型及时转换为包含三个低阶方程的耦合系统。接下来，制定了一种完全离散的混合元素算法，其中时间方向通过二阶方案近似。对所提出的混合方案进行了稳定性分析，并得出了三个函数的最优误差估计。最后，通过数值试验验证了理论结果。