Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems

Jen-Yi Chang, Ru-Yun Chen and Chia-Cheng Tsai
Additional contact information
Jen-Yi Chang: General Education Center, Tainan University of Technology, Tainan 71002, Taiwan
Ru-Yun Chen: Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
Chia-Cheng Tsai: Bachelor Degree Program in Ocean Engineering and Technology, National Taiwan Ocean University, Keelung 202301, Taiwan

Mathematics, 2022, vol. 10, issue 2, 1-20

Abstract: This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

Keywords: radial basis function collocation method; time-dependent convection-diffusion-reaction problem; meshless numerical methods; method of approximate particular solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/2/188/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/2/188/ (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:10:y:2022:i:2:p:188-:d:720089

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 ().