Numerical solution of the Bagley–Torvik equation using shifted Chebyshev operational matrix

Advances in Difference Equations

article

Ji, Tianfu¹  Hou, Jianhua²  Yang, Changqing² 

[1] Department of Science, Lianyungang Technical College;Department of Science, Jiangsu Ocean University

关键词: Bagley–Torvik equation;    Chebyshev polynomials;    Collocation method;    Liouville–Caputo derivative;   

DOI  :  10.1186/s13662-020-03110-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this study, an efficient numerical scheme based on shifted Chebyshev polynomials is established to obtain numerical solutions of the Bagley–Torvik equation. We first derive the shifted Chebyshev operational matrix of fractional derivative. Then, by the use of these operational matrices, we reduce the corresponding fractional order differential equation to a system of algebraic equations, which can be solved numerically by Newton’s method. Furthermore, the maximum absolute error is obtained through error analysis. Finally, numerical examples are presented to validate our theoretical analysis.

【 授权许可】

CC BY