Solution of Finite Difference Method and Differential Quadrature Method in Burgers Equation
Abstract
The Finite Difference Method and Differential Quadrature Method are used to solve the partial differential equation in Burgers equation. The different number of nodes is used in these methods to investigate the accuracy. The solutions of these methods are compared in terms of accuracy of the numerical solution. C language program have been developed based on the method in order to solve the Burgers equation. The results of this study are compared in terms of convergence as well as accuracy of the numerical solution. Generally, from the numerical results show that the Differential Quadrature Method is better than the Finite Different Method in terms of accuracy and convergence
##Keywords:##
Finite Difference Method (FDM), Differential Quadrature Method (DQM), Heat Transfer
Published
Nov 30, 2019
How to Cite
AB. AZIZ, Amiruddin; NGARISAN, Noor Syazana; BAKI, Nur Afriza.
Solution of Finite Difference Method and Differential Quadrature Method in Burgers Equation.
Journal of Ocean, Mechanical and Aerospace -science and engineering-, [S.l.], v. 63, n. 3, p. 1-4, nov. 2019.
ISSN 2527-6085.
Available at: <https://isomase.org/Journals/index.php/jomase/article/view/97>. Date accessed: 19 aug. 2024.
doi: http://dx.doi.org/10.36842/jomase.v63i3.97.
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References
1. Amiruddin Ab. Aziz, Hoe, Y.S., Iskandar, H. and Bahari, A.R. (2016). Application of Finite Difference Method and Differential Quadrature Method in Burgers Equation. Journal of Applied Environmental and Biological Sciences. 6(11), 111-114.
2. Çiçek, Y. and Tanoğlu, G. (2016). Strang Splitting Method for Burgers-Huxley Equation. Applied Mathematics and Computation. 276, 454-467.
3. Sari, M. and Gurarslan, G. (2009). Numerical Solutions of the Generalized Burgers-Huxley Equation by A Differential Quadrature Method. Mathematical Problems in Engineering. 2009, 370765.
4. Wazwaz, A.M. (2009). Burgers, Fisher and Related Equations. In Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Springer, Berlin, Heidelberg
5. Yefimova, O.Y. and Kudryashov, N.A. (2004). Exact Solutions of the Burgers-Huxley Equation. Journal of Applied Mathematics and Mechanics 68(3), 413-420.
6. Gao, H. and Zhao, R.X. (2009). New Exact Solutions to the Generalized Burgers–Huxley Equation. Applied Mathematics and Computer.
7. Shu, C. (2000). Differential Quadrature and Its Application in Engineering. Great Britain: Springer-Verlag London.
8. Mittal, R.C. and Jiwari, R. (2009). Numerical Study of Burgers-Huxley Equation by Differential Quadrature Method. International Journal of Applied Math and Mechanic. 5(8), 1- 9.
9. Ngarisan, N.S. (2016). The Application of Finite Element Method to Solve Heat Transfer Problem Involving 2D Irregular Geometry. Journal of Applied Environmental and Biological Sciences. 6(11S), 23-30.
10. Chen, W. (1996). Differential Quadrature Method and its Applications in Engineering-Applying Special Matrix Product to Nonlinear Computations and Analysis. PhD Thesis. Shanghai Jiao Tong University.
11. Palmer, A.C. and King, R.A. (2008). Subsea Pipeline Engineering: Pennwell Corporation.
12. Bai, Y. and Bai, Q. (2010). Subsea Engineering Handbook: Elsevier.
13. Shao, B., Yan, X. (2011). Reliability Analysis of Locally Thinned Submarine Pipelines in Cheng Dao Oil Field. Applied Mechanics and Materials. 94-96, 1527-1530.
14. Li, Z.G (2010). Configuration of Submarine Pipeline for Deepwater S-Lay Technique. The International Society of Offshore and Polar Engineers.
2. Çiçek, Y. and Tanoğlu, G. (2016). Strang Splitting Method for Burgers-Huxley Equation. Applied Mathematics and Computation. 276, 454-467.
3. Sari, M. and Gurarslan, G. (2009). Numerical Solutions of the Generalized Burgers-Huxley Equation by A Differential Quadrature Method. Mathematical Problems in Engineering. 2009, 370765.
4. Wazwaz, A.M. (2009). Burgers, Fisher and Related Equations. In Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Springer, Berlin, Heidelberg
5. Yefimova, O.Y. and Kudryashov, N.A. (2004). Exact Solutions of the Burgers-Huxley Equation. Journal of Applied Mathematics and Mechanics 68(3), 413-420.
6. Gao, H. and Zhao, R.X. (2009). New Exact Solutions to the Generalized Burgers–Huxley Equation. Applied Mathematics and Computer.
7. Shu, C. (2000). Differential Quadrature and Its Application in Engineering. Great Britain: Springer-Verlag London.
8. Mittal, R.C. and Jiwari, R. (2009). Numerical Study of Burgers-Huxley Equation by Differential Quadrature Method. International Journal of Applied Math and Mechanic. 5(8), 1- 9.
9. Ngarisan, N.S. (2016). The Application of Finite Element Method to Solve Heat Transfer Problem Involving 2D Irregular Geometry. Journal of Applied Environmental and Biological Sciences. 6(11S), 23-30.
10. Chen, W. (1996). Differential Quadrature Method and its Applications in Engineering-Applying Special Matrix Product to Nonlinear Computations and Analysis. PhD Thesis. Shanghai Jiao Tong University.
11. Palmer, A.C. and King, R.A. (2008). Subsea Pipeline Engineering: Pennwell Corporation.
12. Bai, Y. and Bai, Q. (2010). Subsea Engineering Handbook: Elsevier.
13. Shao, B., Yan, X. (2011). Reliability Analysis of Locally Thinned Submarine Pipelines in Cheng Dao Oil Field. Applied Mechanics and Materials. 94-96, 1527-1530.
14. Li, Z.G (2010). Configuration of Submarine Pipeline for Deepwater S-Lay Technique. The International Society of Offshore and Polar Engineers.
