Trigonometric Cubic B-Spline Least Squares Algorithm for Solitary Wave Propagation

DAĞ İ., Ay B., SAKA B., ERSOY HEPSON Ö.

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1002/mma.70338
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

A new variant of least squares algorithm is introduced for obtaining numerical solutions of the regularized long wave equation (RLWE). The Crank-Nicolson method and the least squares method (LSM) are combined to integrate the RLWE in both time and space, respectively. The approximation function for the LSM is a sum of weighted cubic trigonometric B-splines (CTB-splines). Minimization of the Galerkin form of the least squares approach has been carried out using the time weight of the CTB-spline approximation. The propagation of solitary wave solutions and wave undulation are studied to assess the effectiveness of the suggested algorithm.