An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers' equation. Issue 3 (3rd March 2020)

• Record Type: Journal Article
• Authors: Yaseen, Muhammad; Abbas, Muhammad
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 3(2020)
• Page Start: 725
• Page End: 738
• Publication Date: 2020-03-03
• Subjects: Time fractional Burgers' equation -- trigonometric basis functions -- cubic trigonometric B-splines method -- stability -- convergence; 65M70 -- 65Z05 -- 65D05 -- 65D07 -- 35B35; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1612053
• Languages: English
• ISSNs: 0020-7160

Abstract

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.