Applied Numerical Mathematics ( IF 2.2 ) Pub Date : 2021-07-28 , DOI: 10.1016/j.apnum.2021.07.017 Xuhong Yu 1 , Long Li 1 , Zhongqing Wang 1
In this paper, we first introduce three series of Legendre rational basis functions on the half/whole line by the diagonalization technique and the matrix decomposition technique. The new basis functions are mutually orthogonal in both - and -inner products, and lead to diagonal systems for second order problems with constant coefficients. Then we construct efficient space-time spectral methods for parabolic problems in unbounded domains using Legendre rational approximation in space and Legendre-Gauss collocation method in time, which can be implemented in a synchronous parallel fashion. Numerical results demonstrate that the use of simultaneously orthogonal basis functions in space may greatly simplify the implementation of the space-time spectral methods. Using these suggested methods, higher accuracy can also be obtained.
中文翻译:
无界域抛物线问题的高效时空Legendre有理谱方法
在本文中,我们首先通过对角化技术和矩阵分解技术在半/整线上介绍了三个系列的勒让德有理基函数。新的基函数在两者中相互正交- 和 -内积,并导致具有常系数的二阶问题的对角系统。然后,我们使用空间上的勒让德有理逼近和时间上的勒让德-高斯搭配方法,为无界域中的抛物线问题构建了有效的时空谱方法,这些方法可以以同步并行方式实现。数值结果表明,在空间中同时使用正交基函数可以大大简化时空谱方法的实现。使用这些建议的方法,还可以获得更高的准确度。