Vieta–Lucas polynomials for solving a fractional-order mathematical physics model

Advances in Difference Equations

A. A. El-Sayed¹  P. Agarwal² 

[1] Department of Mathematics, Rustaq College of Education, Ministry of Higher Education, 329, Rustaq, Sultanate of Oman;Department of Mathematics, Faculty of Science, Fayoum University, 63514, Fayoum, Egypt;International Center for Basic and Applied Sciences, 302029, Jaipur, India;Department of Mathematics, Anand International College of Engineering, Jaipur, India;

关键词: Advection–dispersion equation of the fractional-order;    Caputo fractional-order operator;    Vieta–Lucas polynomials;    Spectral collocation method;    Nonstandard finite difference method;    65M99;    33C45;    42A10;    65N99;    65Z05;   

DOI  :  10.1186/s13662-020-03085-y

来源: Springer

【 摘 要 】

In this article, a fractional-order mathematical physics model, advection–dispersion equation (FADE), will be solved numerically through a new approximative technique. Shifted Vieta–Lucas orthogonal polynomials will be considered as the main base for the desired numerical solution. These polynomials are used for transforming the FADE into an ordinary differential equations system (ODES). The nonstandard finite difference method coincidence with the spectral collocation method will be used for converting the ODES into an equivalence system of algebraic equations that can be solved numerically. The Caputo fractional derivative will be used. Moreover, the error analysis and the upper bound of the derived formula error will be investigated. Lastly, the accuracy and efficiency of the proposed method will be demonstrated through some numerical applications.

【 授权许可】

CC BY