A Conservative and Implicit Second-Order Nonlinear Numerical Scheme for the Rosenau-KdV Equation

Cui Guo, Yinglin Wang and Yuesheng Luo
Additional contact information
Cui Guo: Harbin Engineering University, Harbin 150001, China
Yinglin Wang: Harbin Engineering University, Harbin 150001, China
Yuesheng Luo: Harbin Engineering University, Harbin 150001, China

Mathematics, 2021, vol. 9, issue 11, 1-15

Abstract: In this paper, for solving the nonlinear Rosenau-KdV equation, a conservative implicit two-level nonlinear scheme is proposed by a new numerical method named the multiple integral finite volume method. According to the order of the original differential equation’s highest derivative, we can confirm the number of integration steps, which is just called multiple integration. By multiple integration, a partial differential equation can be converted into a pure integral equation. This is very important because we can effectively avoid the large errors caused by directly approximating the derivative of the original differential equation using the finite difference method. We use the multiple integral finite volume method in the spatial direction and use finite difference in the time direction to construct the numerical scheme. The precision of this scheme is O ( ? 2 + h 3 ) . In addition, we verify that the scheme possesses the conservative property on the original equation. The solvability, uniqueness, convergence, and unconditional stability of this scheme are also demonstrated. The numerical results show that this method can obtain highly accurate solutions. Further, the tendency of the numerical results is consistent with the tendency of the analytical results. This shows that the discrete scheme is effective.

Keywords: multiple integral finite volume method; finite difference method; Rosenau-KdV; conservation; solvability; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/11/1183/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/11/1183/ (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:9:y:2021:i:11:p:1183-:d:561014

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 ().