Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method

Advances in Difference Equations

article

Majeed, Abdul¹  Kamran, Mohsin¹  Iqbal, Muhammad Kashif²  Baleanu, Dumitru³ 

[1] Department of Mathematics, Division of Science and Technology, University of Education;Department of Mathematics, Government College University;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University;Department of Medical Research, China Medical University Hospital, China Medical University;Institute of Space Sciences

关键词: Cubic B-spline collocation method;    Time fractional differential equation;    Caputo’s fractional derivative;    Stability and convergence;    Finite difference formulation;   

DOI  :  10.1186/s13662-020-02619-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank–Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers’ and Fisher’s equations. The error norms $L_{2}$ and $L_{\infty }$ have been calculated to validate the efficiency and accuracy of the presented algorithm.

【 授权许可】

CC BY