Space-time polynomial particular solutions method for solving time-dependent problems
Space-time polynomial particular solutions method for solving time-dependent problems
复制标题
求解瞬态问题的时空多项式特解法
DOI：
10.1080/10407790.2019.1693199
复制
发表时间：
2020
影响因子：
1
通讯作者：
Zheng Hui
中科院分区：
文献类型：
--
作者：
Cao Yanhua;Chen C. S.;Zheng Hui
提出了一种以多项式为基函数求解含时问题的新的时空方法。我们提出的方法不存在稳定性问题，也不需要时空径向基函数方法中所需的任何参数，如形状参数或节点分布参数。本文用新的时空方法考虑了不规则和规则空域上的各种线性和非线性数值算例。实验结果表明，该方法具有较高的精度和稳定性。
A new space–time method, utilizing polynomials as the basis function, has been developed for solving time-dependent problems. Our proposed method does not have stability issues, nor does it require any parameters as were needed in the space–time radial basis function method, such as, the shape parameter, or those for the nodes distribution. In this article, various linear and nonlinear numerical examples on irregular and regular space domains are considered by the new space–time method. The results obtained demonstrate that our proposed method is stable and highly accuracy.