Numerical Gradient Schemes for Heat Equations Based on the Collocation Polynomial and Hermite Interpolation

Hou-Biao Li, Ming-Yan Song, Er-Jie Zhong and Xian-Ming Gu
Additional contact information
Hou-Biao Li: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Ming-Yan Song: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Er-Jie Zhong: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Xian-Ming Gu: School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Mathematics, 2019, vol. 7, issue 1, 1-22

Abstract: As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is that it is unconditionally stable and convergent on the order O ( τ 2 + h 4 ) (where τ is the time step size and h is the mesh size), under the maximum norm for a class of nonlinear delay partial differential equations with initial and Dirichlet boundary conditions. In this article, a new numerical gradient scheme based on the collocation polynomial and Hermite interpolation is presented. The convergence order of this kind of method is also O ( τ 2 + h 4 ) under the discrete maximum norm when the spatial step size is twice the one of H-OCD, which accelerates the computational process. In addition, some corresponding analyses are made and the Richardson extrapolation technique is also considered in the time direction. The results of numerical experiments are consistent with the theoretical analysis.

Keywords: heat equation; compact difference schemes; numerical gradient; collocation polynomial; Hermite interpolation; Richardson extrapolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/1/93/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/1/93/ (text/html)

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:gam:jmathe:v:7:y:2019:i:1:p:93-:d:198502

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().