Numerical solutions of time fractional Burgers' equation involving Atangana-Baleanu derivative via cubic B-spline functions

被引：35

作者：

Shafiq, Madiha ^{[1
]}

Abbas, Muhammad ^{[1
]}

Abdullah, Farah Aini ^{[2
]}

Majeed, Abdul ^{[3
]}

Abdeljawad, Thabet ^{[4
,5
]}

Alqudah, Manar A. ^{[6
]}

机构：

[1] Univ Sargodha, Dept Math, Sargodha 40100, Pakistan

[2] Univ Sains Malaysia, Sch Math Sci, George Town 11800, Malaysia

[3] Univ Educ, Dept Math, Div Sci & Technol, Lahore 54770, Pakistan

[4] Prince Sultan Univ, Dept Math & Sci, Riyadh 11586, Saudi Arabia

[5] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

[6] Princess Nourah Bint Abdulrahman Univ, Fac Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia

来源：

RESULTS IN PHYSICS | 2022年 / 34卷

关键词：

Burgers' equation; Atangana-Baleanu fractional derivative; Spline interpolation; Cubic B-spline functions; Finite difference technique; Stability; Convergence; DIFFERENTIAL QUADRATURE METHOD; COLLOCATION METHOD; KERNEL;

D O I：

10.1016/j.rinp.2022.105244

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The current paper uses the cubic B-spline functions and -weighted scheme to achieve numerical solutions of the time fractional Burgers' equation with Atangana-Baleanu derivative. A non-singular kernel is involved in the Atangana-Baleanu fractional derivative. For discretization along temporal and spatial grids, the proposed numerical technique employs the finite difference approach and cubic B-spline functions, respectively. This scheme is unconditionally stable and second order convergent in spatial and temporal directions. The presented approach is endorsed by some numerical examples, which show that it is applicable and accurate.

引用

页数：16

共 44 条

[11] Parametric spline functions for the solution of the one time fractional Burgers' equation [J].