Abstract 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.

中文翻译：

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求解瞬态问题的时空多项式特解法

摘要 一种新的时空方法，利用多项式作为基函数，已被开发用于解决与时间相关的问题。我们提出的方法没有稳定性问题，也不需要时空径向基函数方法中需要的任何参数，例如形状参数或节点分布的参数。在本文中，通过新的时空方法考虑了不规则和规则空间域上的各种线性和非线性数值例子。获得的结果表明，我们提出的方法稳定且准确度高。