Time-dependent Hermite–Galerkin spectral method and its applications

Xue Luo, Shing-Tung Yau and Stephen S.-T. Yau

Applied Mathematics and Computation, 2015, vol. 264, issue C, 378-391

Abstract: A time-dependent Hermite–Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection–diffusion equations in the unbounded domains. The time-dependent scaling factor and translating factor are introduced in the definition of the generalized Hermite functions (GHF). As a consequence, the THGSM based on these GHF has many advantages, not only in theoretical proofs, but also in numerical implementations. The stability and spectral convergence of our proposed method have been established in this paper. The Korteweg–de Vries–Burgers (KdVB) equation and its special cases, including the heat equation and the Burgers’ equation, as the examples, have been numerically solved by our method. The numerical results are presented, and it surpasses the existing methods in accuracy. Our theoretical proof of the spectral convergence has been supported by the numerical results.

Keywords: Hermite–Galerkin spectral method; Time-dependent parameters; Nonlinear convection–diffusion equations (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315005500
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:264:y:2015:i:c:p:378-391

DOI: 10.1016/j.amc.2015.04.088

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().