Numerical solution of unperturbed and general perturbed Newell–Whitehead–Segel equation by the local discontinuous Galerkin method

S. Saha Ray and Abhilash Chand
Additional contact information
S. Saha Ray: Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, Odisha, India
Abhilash Chand: Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, Odisha, India

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 04, 1-17

Abstract: This paper investigates numerical solutions for the unperturbed and general perturbed Newell–Whitehead–Segel-type equations with the help of the local discontinuous Galerkin method. The stability analysis and error estimations of the proposed local discontinuous Galerkin algorithm are extensively examined. First, the spatial variables are discretized to provide a semidiscrete method of lines scheme. This generates an ordinary differential equation system in the temporal variable, which is subsequently solved using the total variation diminishing Runge–Kutta method of higher order. The generated numerical results are compared to the exact results and a few other existing numerical methods via various tables and figures to illustrate the efficiency and accuracy of the proposed method. The numerical results show that the proposed method is an effective numerical scheme for solving the Newell–Whitehead–Segel equation since the solutions obtained using the local discontinuous Galerkin method are highly close to the exact solutions with significantly less error.

Keywords: Newell–Whitehead–Segel equation; local discontinuous Galerkin method; stability analysis; Runge–Kutta method (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183123500493
Access to full text is restricted to subscribers

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:wsi:ijmpcx:v:34:y:2023:i:04:n:s0129183123500493

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183123500493

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().