文章基本信息

标题：Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation
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作者：M. A. Zaky ; D. Baleanu ; J. F. Alzaidy 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：102
DOI：10.1186/s13662-018-1561-7
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate numerical solution of the variable-order fractional Galilei advection–diffusion equation with a nonlinear source term. The suggested method is based on the shifted Legendre collocation procedure and a matrix form representation of variable-order Caputo fractional derivative. The main advantage of the proposed method is investigating a global approximation for the spatial and temporal discretizations. This method reduces the problem to a system of algebraic equations, which is easier to solve. The validity and effectiveness of the method are illustrated by an easy-to-follow example.
关键词：Variable-order derivative ; Nonlinear Galilei invariant advection–diffusion equation ; Collocation method ; Legendre polynomials