摘要: 为了克服波动方程经典显式差分法条件稳定的限制，本文将建立和分析一维非线性耦合波动方程组的Du Fort-Frankel (DFF)格式。在耦合波动方程组经典显式差分格式的基础上，对二阶中心差分算子提出了一类改进的差分公式，从而建立了具有更好稳定性的DFF格式。运用了能量分析法证明了由当前算法得到的数值解在无穷范数意义下有
的收敛阶。最后，数值结果验证了格式的有效性和理论结果的正确性。
Abstract:
In order to overcome the limitation of the stability condition of the classical explicit difference method for wave equations, this paper is concerned with the development and analysis of an unconditionally stable Du Fort Frankel (DFF) scheme for coupled wave equations. Based on the classical explicit difference scheme for coupled wave equations, a DFF scheme with better stability is derived by improving the central difference operator. By using the discrete energy method, it is shown that numerical solutions obtained by the current method are convergent with an order of
in maximum norm. Finally, numerical results verify the validity of the scheme and the correctness of the theoretical results.