Work

Numerical solution of seventh order KdV equations via quintic B-splines collocation method

Year: 2024

Type: article

Abstract: This paper proposes an approach based on the collocation technique with fifth-degree B-splines to numerically solve higher-order Korteweg–de-Vries (KdV) equations. The discretization of the temporal part is performed via a finite difference scheme and the quintic B-spline approximates the function and its derivatives. Consequently, the equation leads to an algebraic system being solved using matrices. The stability of the proposed scheme is also discussed and is found to be unconditionally stable. The solved test problems exhibit the accuracy and stability of the technique. The error is computed using the L ∞ norm and the L 2 norm. When compared to previous results, the observations suggest that the technique is better than many other methods present in the literature.

Source: Alexandria Engineering Journal

DOI: 10.1016/j.aej.2024.11.098

Authors: Sirajul Haq, Ayesha Noreen, Tanveer Akbar, Shams Ul Arifeen, Abdul Ghafoor, Zareen A. Khan

Institutions: Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, National University of Computer and Emerging Sciences, Kohat University of Science and Technology, Princess Nourah bint Abdulrahman University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,300

Funder: Princess Nourah Bint Abdulrahman University