Abstract
In
this study, a high accurate numerical solution of the Burgers’ equation is
obtained. For this, the collocation method based on quintic B-spline functions
for space discretization and the fourth-order single step method for time
discretization are used. In order to see the efficiency of the algorithm, a
test problem with an analytical solution is discussed and compared with the
numerical solution obtained.
Keywords
Burgers' equation Collocation method fourth order single step method quintic B-spline functions
References
- Bateman H. Some recent researches on the motion of the fluids, Monthly Weather Review. 43 163-70, 1915.
- Burgers J.M. A mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics. 1 171-199, 1948.
- Yang X., Ge Y., Zhang L. A class of high-order compact difference schemes for solving the Burgers’ equations, Applied Mathematics and Computation. 358 394-417, 2019.
- Fu F., Li J., Lin J., Guan Y., Gao F., Zhang C., Chen L. Moving least squares particle hydrodynamics method for Burgers’ equation, Applied Mathematics and Computation. 356 362-378, 2019.
- Sari M., Tunc H., Seydaoglu M. Higher order splitting approaches in analysis of the Burgers equation, Kuwait Journal of Science. 46 1-14, 2019.
- Rathore S., Saraswat G.K. Homotopy perturbation approach to the solution of non-linear Burgers’s equation, International Journal of Mathematics and its Applications. 6 203-211, 2018.
- Mohamed N.A. Fully implicit scheme for solving Burgers' equation based on finite difference method. The Egyptian International Journal of Engineering Sciences & Technology. 26 38-44, 2018
- Aswin V.S., Awasthi A., Rashidi M.M. A differential quadrature based numerical method for highly accurate solutions of Burgers' equation, Numerical Methods for Partial Differential Equations. 33 2023-2042, 2017.
- Tamsir M., Srivastava V.K., Jiwari R. An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation, Applied Mathematics and Computation. 290 111-124, 2016.
Abstract
Bu
çalışmada, Burgers denkleminin yüksek doğruluklu bir sayısal çözümü elde
edilmiştir. Bunun için, konum ayrıştırmasında quintic B-spline fonksiyonlarını
temel alan kolokasyon yöntemi ve zaman ayrıştırmasında dördüncü dereceden tek
adımlı yöntem kullanılmıştır. Algoritmanın etkinliğini görmek için, analitik
çözüme sahip bir test problemi ele alınmış ve elde edilen sayısal çözümler ile
karşılaştırılmıştır.
Keywords
Burgers denklemi Dördüncü dereceden tek adımlı yöntem Kolokasyon metodu Kuintik B-spline fonksiyonları
References
- Bateman H. Some recent researches on the motion of the fluids, Monthly Weather Review. 43 163-70, 1915.
- Burgers J.M. A mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics. 1 171-199, 1948.
- Yang X., Ge Y., Zhang L. A class of high-order compact difference schemes for solving the Burgers’ equations, Applied Mathematics and Computation. 358 394-417, 2019.
- Fu F., Li J., Lin J., Guan Y., Gao F., Zhang C., Chen L. Moving least squares particle hydrodynamics method for Burgers’ equation, Applied Mathematics and Computation. 356 362-378, 2019.
- Sari M., Tunc H., Seydaoglu M. Higher order splitting approaches in analysis of the Burgers equation, Kuwait Journal of Science. 46 1-14, 2019.
- Rathore S., Saraswat G.K. Homotopy perturbation approach to the solution of non-linear Burgers’s equation, International Journal of Mathematics and its Applications. 6 203-211, 2018.
- Mohamed N.A. Fully implicit scheme for solving Burgers' equation based on finite difference method. The Egyptian International Journal of Engineering Sciences & Technology. 26 38-44, 2018
- Aswin V.S., Awasthi A., Rashidi M.M. A differential quadrature based numerical method for highly accurate solutions of Burgers' equation, Numerical Methods for Partial Differential Equations. 33 2023-2042, 2017.
- Tamsir M., Srivastava V.K., Jiwari R. An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation, Applied Mathematics and Computation. 290 111-124, 2016.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 26, 2019 |
| Published in Issue | Year 2019 |