A time-space quadratic-extended cubic B-spline integrators for the Burgers’ equation

DAĞ İ., Uğurluoğlu S.

Physica Scripta, vol.101, no.15, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 101 Issue: 15
  • Publication Date: 2026
  • Doi Number: 10.1088/1402-4896/ae5692
  • Journal Name: Physica Scripta
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
  • Keywords: bspline, Burgers’ equation, collocation
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

A new numerical method is presented for the solution of the Burgers’ equation(BE). Quadratic B-splines are used for the time integration of the Burgers’ equation, while the spatial integration is handled using extended cubic B-spline collocation method. Thus, a combination of both quadratic and cubic B-spline collocation methods is utilized to obtain a system of algebraic equations, which is then solved to find the solutions of the BE. The applicability and simplicity of the proposed algorithm are demonstrated through three test problems