非线性延迟波动方程的紧致有限差分格式
A Compact Finite Difference Scheme for Nonlinear Wave Equation with Delay
摘要: 本文主要研究了一类带有Dirichlet边界条件的非线性延迟波动方程，并建立了一个紧致有限差分格式。运用离散能量法证明了该差分格式在L∞范数下满足时间二阶、空间四阶的收敛率。最后通过数值算例验证了算法的精度和有效性。
Abstract: A compact finite difference scheme is established for a class of nonlinear wave equations with delay with Dirichlet boundary value conditions. By using the discrete energy method, the proposed compact finite difference scheme is proved temporally second-order convergence rate and spatially fourth-order convergence rate in L∞ norm. Finally, numerical results have confirmed the accuracy and effectiveness of the algorithm.
文章引用：罗雲榕, 王子哲, 王博. 非线性延迟波动方程的紧致有限差分格式[J]. 理论数学, 2022, 12(5): 714-722. https://doi.org/10.12677/PM.2022.125082

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