New trigonometric B-spline approximation for numerical investigation of the regularized long-wave equation

• Published in: Open Physics 2021-12, Vol.19 (1), p.758-769
• Main Authors: Msmali, Ahmed Hussein, Tamsir, Mohammad, Dhiman, Neeraj, Aiyashi, Mohammed A.
• Format: Article
• Language: English
• Subjects: collocation technique; NCTB-spline functions; RLW equation; Rubin–Graves-type linearization technique; stability analysis
• ISSN: 2391-5471; 2391-5471
• DOI: 10.1515/phys-2021-0087

The objective of this work is to propose a collocation technique based on new cubic trigonometric B-spline (NCTB-spline) functions to approximate the regularized long-wave (RLW) equation. This equation is used for modelling numerous problems occurring in applied sciences. The NCTB-spline collocation method is used to integrate the spatial derivatives. We use the Rubin–Graves linearization technique to linearize the non-linear term. The accuracy and efficiency of the technique are examined by employing it on three important numerical examples which have three invariants of motion . mass, momentum, and energy. It is observed that the error norms of the present method are less than the error norms of the methods available in the literature. The numerical values of these invariants have also been approximated, which remain conserved during the program run which shows that the propagation of the solitary wave is represented perfectly. The propagation of one and two solitary waves and undulations of waves are depicted graphically. The stability analysis shows that the method is unconditionally stable.