Numerical Solutions of Third-Order Time-Fractional Differential Equations Using Cubic B-Spline Functions

被引:6
|
作者
Abbas, Muhammad [1 ]
Bibi, Afreen [1 ]
Alzaidi, Ahmed S. M. [2 ]
Nazir, Tahir [1 ]
Majeed, Abdul [3 ]
Akram, Ghazala [4 ]
机构
[1] Univ Sargodha, Dept Math, Sargodha 40100, Pakistan
[2] Taif Univ, Coll Sci, Dept Math & Stat, POB 11099, Taif 21944, Saudi Arabia
[3] Univ Educ, Dept Math, Div Sci & Technol, Lahore 54770, Pakistan
[4] Univ Punjab, Dept Math, Lahore 54590, Pakistan
关键词
cubic B-spline functions; third-order time-fractional partial differential equation; Caputo's time fractional derivative; stability; convergence; Crank-Nicholson finite difference scheme; DIFFUSION; TRANSPORT;
D O I
10.3390/fractalfract6090528
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Numerous fields, including the physical sciences, social sciences, and earth sciences, benefit greatly from the application of fractional calculus (FC). The fractional-order derivative is developed from the integer-order derivative, and in recent years, real-world modeling has performed better using the fractional-order derivative. Due to the flexibility of B-spline functions and their capability for very accurate estimation of fractional equations, they have been employed as a solution interpolating polynomials for the solution of fractional partial differential equations (FPDEs). In this study, cubic B-spline (CBS) basis functions with new approximations are utilized for numerical solution of third-order fractional differential equation. Initially, the CBS functions and finite difference scheme are applied to discretize the spatial and Caputo time fractional derivatives, respectively. The scheme is convergent numerically and theoretically as well as being unconditionally stable. On a variety of problems, the validity of the proposed technique is assessed, and the numerical results are contrasted with those reported in the literature.
引用
收藏
页数:17
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