Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation
Abstract 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 fraction...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1561-7 |
| _version_ | 1819052937028042752 |
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| author | M. A. Zaky D. Baleanu J. F. Alzaidy E. Hashemizadeh |
| author_facet | M. A. Zaky D. Baleanu J. F. Alzaidy E. Hashemizadeh |
| author_sort | M. A. Zaky |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-21T12:27:46Z |
| format | Article |
| id | doaj.art-e0f6155ddcd7466c8536784e5f17cfe8 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-21T12:27:46Z |
| publishDate | 2018-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-e0f6155ddcd7466c8536784e5f17cfe82022-12-21T19:04:08ZengSpringerOpenAdvances in Difference Equations1687-18472018-03-012018111110.1186/s13662-018-1561-7Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equationM. A. Zaky0D. Baleanu1J. F. Alzaidy2E. Hashemizadeh3Department of Applied Mathematics, National Research CentreDepartment of Mathematics, Cankaya UniversityDepartment of Mathematics, Faculty of Science, King Abdulaziz UniversityDepartment of Mathematics, Karaj Branch, Islamic Azad UniversityAbstract 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.http://link.springer.com/article/10.1186/s13662-018-1561-7Variable-order derivativeNonlinear Galilei invariant advection–diffusion equationCollocation methodLegendre polynomials |
| spellingShingle | M. A. Zaky D. Baleanu J. F. Alzaidy E. Hashemizadeh Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation Advances in Difference Equations Variable-order derivative Nonlinear Galilei invariant advection–diffusion equation Collocation method Legendre polynomials |
| title | Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation |
| title_full | Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation |
| title_fullStr | Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation |
| title_full_unstemmed | Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation |
| title_short | Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation |
| title_sort | operational matrix approach for solving the variable order nonlinear galilei invariant advection diffusion equation |
| topic | Variable-order derivative Nonlinear Galilei invariant advection–diffusion equation Collocation method Legendre polynomials |
| url | http://link.springer.com/article/10.1186/s13662-018-1561-7 |
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