An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers' equation

ABSTRACT

This paper presents a computational technique based on cubic trigonometric B-splines for the time fractional Burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient and significantly reduces the computational cost. The usual finite difference formulation is used to approximate the Caputo time fractional derivative while the derivative in space is discretized using cubic trigonometric B-spline functions. The proposed technique is proved to be globally unconditionally stable. A convergence analysis is discussed to measure the accuracy of the solution. Computational experiments are performed to further confirm the accuracy and stability of the method. Numerical results are compared with those obtained by a scheme based on parametric spline functions. The comparison reveals that the proposed scheme is quite accurate and effective.

KEYWORDS:

• Time fractional Burgers' equation
• trigonometric basis functions
• cubic trigonometric B-splines method
• stability
• convergence

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M70
• 65Z05
• 65D05
• 65D07
• 35B35

Acknowledgements

The authors are grateful to the anonymous reviewers for their helpful and valuable comments/suggestions in the improvement of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Muhammad Yaseen  http://orcid.org/0000-0001-7999-2847

Muhammad Abbas  http://orcid.org/0000-0002-0491-1528