当前位置: X-MOL 学术Mathematics › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods
Mathematics ( IF 2.4 ) Pub Date : 2021-05-14 , DOI: 10.3390/math9101113
Isaías Alonso-Mallo , Ana M. Portillo

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrarily high-order splitting scheme. We propose a technique to incorporate the boundary values that is more accurate than the one obtained in the standard way, which is clearly seen in the numerical experiments. We prove the consistency and convergence, with the same order of the splitting method, of the full discretization carried out with this technique. Although we performed mathematical analysis under the hypothesis that the source term was Lipschitz-continuous, numerical experiments show that this technique works in more general cases.

中文翻译:

使用任意高阶分裂方法将半线性波动问题与时变边界值积分

通过使用线法来近似与具有随时间变化的边界值的半线性波动方程有关的初始边界值问题。时间积分是通过从任意高阶分割方案中获得的显式时间方法来实现的。我们提出了一种合并边界值的技术,该技术比以标准方式获得的边界值更准确,这在数值实验中可以清楚地看到。我们证明了采用该方法进行完全离散化的一致性和收敛性,采用的分割方法顺序相同。尽管我们在源项为Lipschitz连续的假设下进行了数学分析,但数值实验表明,该技术在更一般的情况下有效。
更新日期:2021-05-14
down
wechat
bug