A comprehensive study of subdivision collocation method for Burgers’ equation

Abstract

This study explores the use of subdivision schemes to efficiently solve Burgers’ equation. Burgers’ equation is a fundamental fluid dynamics equation that describes the nonlinear behavior of fluid flow. This type of nonlinear equation is difficult to solve analytically, which makes the numerical solution an important tool. The subdivision collocation method (SCM) converts Burgers’ equation into a system of algebraic linear equations using the quasilinearization technique. The results of this study demonstrate that the proposed approach yields accurate numerical solutions for Burgers’ equation. Additionally, the subdivision approach is computationally efficient and requires fewer computational resources than existing numerical methods, making it a promising tool for solving Burgers’ equation in practical applications. Overall, this study provides valuable insights into the approximate solution of Burgers’ equation by implementing subdivision schemes.

Keywords:

• Burgers’ equation
• collocation algorithm
• stability
• subdivision schemes

MSc 2020 Subject Classifications:

• 35Q53
• 65L60
• 65D17

Availability of data and materials

The data used to support the findings of the study are available within this paper.

Acknowledgments

All authors have accepted responsibility for the entire content and have approved the final version of the manuscript.

Authors’ contributions

Conceptualization, Syeda Tehmina Ejaz and Ali Akg $\ddot{u}$ l; Formal analysis, Saima Bibi and Murad Khan Hassani; Methodology, Syeda Tehmina Ejaz and Saima Bibi; Supervision, Syeda Tehmina Ejaz; Writing original draft, Saima Bibi and Syeda Tehmina Ejaz; Writing, review and editing, Syeda Tehmina Ejaz, Saima Bibi, Ali Akg $\ddot{u}$l and Murad Khan Hassani.

Disclosure statement

“The authors declare that there are no competing interest regarding the publication of this paper”.

Additional information

Funding

No funds are available for this manuscript.