A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations
In this study, a new composite algorithm with the help of the finite difference and the modified cubic trigonometric B-spline differential quadrature method is developed. The developed method was applied to two-dimensional coupled Burgers’ equation with initial and Dirichlet boundary conditions for...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7240300 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849404791565844480 |
|---|---|
| author | Vikas Kumar Sukhveer Singh Mehmet Emir Koksal |
| author_facet | Vikas Kumar Sukhveer Singh Mehmet Emir Koksal |
| author_sort | Vikas Kumar |
| collection | DOAJ |
| description | In this study, a new composite algorithm with the help of the finite difference and the modified cubic trigonometric B-spline differential quadrature method is developed. The developed method was applied to two-dimensional coupled Burgers’ equation with initial and Dirichlet boundary conditions for computational modeling. The established algorithm is better than the traditional differential quadrature algorithm proposed in literature due to more smoothness of cubic trigonometric B-spline functions. In the development of the algorithm, the first step is semidiscretization in time with the forward finite difference method. Furthermore, the obtained system is fully discretized by the modified cubic trigonometric B-spline differential quadrature method. Finally, we obtain coupled Lyapunov systems of linear equations, which are analyzed by the MATLAB solver for the system. Moreover, comparative study of these solutions with the numerical and exact solutions which are appeared in the literature is also discussed. Finally, it is found that there is good suitability between exact solutions and numerical solutions obtained by the developed composite algorithm. The technique can be extended for various multidimensional Burgers’ equations after some modifications. |
| format | Article |
| id | doaj-art-9aa6530dc8df4dc5959714d392ceb990 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9aa6530dc8df4dc5959714d392ceb9902025-08-20T03:36:53ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/72403007240300A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ EquationsVikas Kumar0Sukhveer Singh1Mehmet Emir Koksal2Department of Mathematics, D. A. V. College Pundri, Kaithal 136026, Haryana, IndiaDepartment of Mathematics, Indian Institute of Technology, Roorkee 247667, IndiaDepartment of Mathematics, Ondokuz Mayıs University, Atakum, Samsun 55139, TurkeyIn this study, a new composite algorithm with the help of the finite difference and the modified cubic trigonometric B-spline differential quadrature method is developed. The developed method was applied to two-dimensional coupled Burgers’ equation with initial and Dirichlet boundary conditions for computational modeling. The established algorithm is better than the traditional differential quadrature algorithm proposed in literature due to more smoothness of cubic trigonometric B-spline functions. In the development of the algorithm, the first step is semidiscretization in time with the forward finite difference method. Furthermore, the obtained system is fully discretized by the modified cubic trigonometric B-spline differential quadrature method. Finally, we obtain coupled Lyapunov systems of linear equations, which are analyzed by the MATLAB solver for the system. Moreover, comparative study of these solutions with the numerical and exact solutions which are appeared in the literature is also discussed. Finally, it is found that there is good suitability between exact solutions and numerical solutions obtained by the developed composite algorithm. The technique can be extended for various multidimensional Burgers’ equations after some modifications.http://dx.doi.org/10.1155/2021/7240300 |
| spellingShingle | Vikas Kumar Sukhveer Singh Mehmet Emir Koksal A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations Journal of Mathematics |
| title | A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations |
| title_full | A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations |
| title_fullStr | A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations |
| title_full_unstemmed | A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations |
| title_short | A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations |
| title_sort | composite algorithm for numerical solutions of two dimensional coupled burgers equations |
| url | http://dx.doi.org/10.1155/2021/7240300 |
| work_keys_str_mv | AT vikaskumar acompositealgorithmfornumericalsolutionsoftwodimensionalcoupledburgersequations AT sukhveersingh acompositealgorithmfornumericalsolutionsoftwodimensionalcoupledburgersequations AT mehmetemirkoksal acompositealgorithmfornumericalsolutionsoftwodimensionalcoupledburgersequations AT vikaskumar compositealgorithmfornumericalsolutionsoftwodimensionalcoupledburgersequations AT sukhveersingh compositealgorithmfornumericalsolutionsoftwodimensionalcoupledburgersequations AT mehmetemirkoksal compositealgorithmfornumericalsolutionsoftwodimensionalcoupledburgersequations |