A Mesh-Free Collocation Method Based on RBFs for the Numerical Solution of Hunter–Saxton and Gardner Equations

Rahman Ullah, Ihteram Ali, Sadaf Shaheen, Tahir Khan, Faizullah Faiz, Hamid Rahman and Tudor Barbu

Mathematical Problems in Engineering, 2022, vol. 2022, 1-11

Abstract: In this paper, the radial basis function (RBF) collocation method is applied to solve nonlinear partial differential equations (PDEs). First, the given equation is reduced to time-discrete form using Ө-weighted scheme. Then, with the help of RBFs, the given PDEs are transformed into a system of algebraic equations that is easy to solve. The proposed technique is verified by solving Hunter–Saxton and Gardner equations. For the solution of these problems, three types of RBFs, including multiquadric (MQ), inverse multiquadric (IMQ), and Gaussian (GA) have been used. The obtained solution is validated with the help of absolute error, L2, and L∞ error norms. The involved shape parameter is selected by the automatic algorithm that lies in the stable region of the method. The stability of the scheme is discussed by the spectral matrix method and validated computationally.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/mpe/2022/2152565.pdf (application/pdf)
http://downloads.hindawi.com/journals/mpe/2022/2152565.xml (application/xml)

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:hin:jnlmpe:2152565

DOI: 10.1155/2022/2152565

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().