دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات43
تعداد شماره‌ها1,224
تعداد مقالات15,035
تعداد مشاهده مقاله50,551,620
تعداد دریافت فایل اصل مقاله13,644,676
Cicek, Yesim, Gucuyenen Kaymak, Nurcan, Bahar, Ersin, Gurarslan, Gurhan, Tangolu, Gamze. (1401). A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation. سامانه مدیریت نشریات علمی, 11(1), 130-142. doi: 10.22034/cmde.2022.50940.2121
Yesim Cicek; Nurcan Gucuyenen Kaymak; Ersin Bahar; Gurhan Gurarslan; Gamze Tangolu. "A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation". سامانه مدیریت نشریات علمی, 11, 1, 1401, 130-142. doi: 10.22034/cmde.2022.50940.2121
Cicek, Yesim, Gucuyenen Kaymak, Nurcan, Bahar, Ersin, Gurarslan, Gurhan, Tangolu, Gamze. (1401). 'A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation', سامانه مدیریت نشریات علمی, 11(1), pp. 130-142. doi: 10.22034/cmde.2022.50940.2121
Cicek, Yesim, Gucuyenen Kaymak, Nurcan, Bahar, Ersin, Gurarslan, Gurhan, Tangolu, Gamze. A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation. سامانه مدیریت نشریات علمی, 1401; 11(1): 130-142. doi: 10.22034/cmde.2022.50940.2121

A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation

Computational Methods for Differential Equations
مقاله 10، دوره 11، شماره 1، فروردین 2023، صفحه 130-142    اصل مقاله (1.4 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50940.2121
نویسندگان
Yesim Cicek1؛ Nurcan Gucuyenen Kaymak* 2؛ Ersin Bahar3؛ Gurhan Gurarslan3؛ Gamze Tangolu4
1Engineering Sciences, Faculty of Architecture and Engineering, Izmir Katip Celebi University, Izmir, Turkey.
2Management Information Systems, Faculty of Economics and Administrative Sciences, Dogus University, Istanbul, Turkey.
3Department of Civil Engineering, Pamukkale University, Denizli, Turkey.
4Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey.
چکیده
In this article, the coupled Burger’s equation which is one of the known systems of the nonlinear parabolic partial differential equations is studied. The method presented here is based on a combination of the quintic B-spline and a high order time integration scheme known as adaptive Runge-Kutta method. First of all, the application of the new algorithm on the coupled Burger’s equation is presented. Then, the convergence of the algorithm is studied in a theorem. Finally, to test the efficiency of the new method, coupled Burger’s equations in literature are studied. We observed that the presented method has better accuracy and efficiency compared to the other methods in the literature.
کلیدواژه‌ها
Quintic B-Spline؛ Adaptive Runge-Kutta method؛ Coupled Burger’s equation؛ Non-linear parabolic partial differential equation
مراجع
  • [1] H. Ahmad, T. A. Khan, and C. Cesarano, Numerical solutions of coupled Burger’s equations, Axioms, 8(4) (2019), 119.
  • [2] E. Bahar and G. Gurarslan, B-spline method of lines for simulation of contaminant transport in groundwater, Water, 12(1607) (2020), 1–21.
  • [3] S. Bak, P. Kim, and D. Kim, A semi-lagrangian approach for numerical simulation of coupled Burgers’ equations, Commun. Nonlinear Sci. Numer. Simulation, 69 (2019), 31–44.
  • [4] K. Burrage, W. H. Hunndsdorfer, and J. G. Verwer, A study of b-convergence of runge-kutta methods, Computing, 36 (1986), 17–34.
  • [5] J. C. Butcher, Implicit runge-kutta processes, Mathematics of Computation, 18(85) (1964), 50–64.
  • [6] J. R. Dormand and P. J. Prince, A family of embedded runge-kutta formulae, Journal of Computation and Applied Mathematics, 6(1) (1980), 19–26.
  • [7] S. E. Esipov, Coupled burgers equations: A model of polydispersive sedimentation, Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 52(4) (1995), 3711–3718.
  • [8] D. Irk, I. Dag, and M. Tombul, Extended cubic b-spline solution of the advection-diffusion equation, KSCE J. Civ. Eng., 19(4) (2014), 929–934.
  • [9] S. U. Islam, S. Haq, and M. Uddin, A meshfree interpolation method for the numerical solution of the coupled nonlinear partial differential equations, Eng. Anal. Bound. Elem., 33(3) (2009), 399–409.
  • [10] D. Kaya, An explicit solution of coupled viscous burgers’ equation by the decomposition method, Int. J. Math. and Math. Sci., 27(11) (2001), 675–680.
  • [11] A. H. Khater, R. S. Temsah, and M. M. Hassan, A chebyshev spectral collocation method for solving Burgers’-type equations, J. Comput. Appl. Math., 222(2), 333–350.
  • [12] A. Korkmaz and I. Dag, Quartic and quintic b-spline methods for advection–diffusion equation, Appl. Math. Comput., 274(1) (2016), 208–219.
  • [13] M. Kumar and S. Pandit, A composite numerical scheme for the numerical simulation of coupled Burgers’ equation, Comput. Phys. Commun., 185(3) (2014), 809–817.
  • [14] R. C. Mittal and G. Arora, Numerical solution of the coupled viscous Burgers’ equation, Commun. Nonlinear Sci. Numer. Simul., 16(3) (2011), 1304–1313.
  • [15] R. C. Mittal and R. Jiwari, Differential quadrature method for numerical solution of coupled viscous Burgers equations, Int. Journal for Comp. Methods in Eng. Science and Mechanics, 13(2) (2012), 88–92.
  • [16] R. C. Mittal and A. Tripathi, A collocation method for numerical solutions of coupled Burgers’ equations, Int. Journal for Comp. Methods in Eng. Science and Mechanics, 15(5) (2014), 457-471.
  • [17] T. Nazir, M. Abbas, A. I. M. Ismail, A. A. Majid, and A. Rashid, The numerical solution of advection—diffusion problems using new cubic trigonometric b-splines approach, Appl. Math. Model., 40(7-8) (2016), 4586–4611.
  • [18] K. R. Raslan, T. E. Danaf, and K. K. Ali, Collocation method with quintic b-spline method for solving coupled Burger’s equations, Fast East Jour. of App. Math., 96(1) (2017), 55–75.
  • [19] A. Rashid and A. I. B. M. Ismail, A fourier pseudospectral method for solving coupled viscous Burgers equations, Comput. Methods in Appl. Math., 9(4) (2009), 412–420.
  • [20] A. Rashid, M. Abbas, A. I. M. Ismail, and A. A. Majid, Numerical solution of the coupled viscous Burgers equations by chebyshev legendre pseudo-spectral method, Appl. Math. Comput., 245 (2014), 372-381.
  • [21] Y. Zhang, J. Lin, S. Reutskiy, H. Sun, and W. Feng, The improved backward substitution method for the simulation of time-dependent nonlinear coupled Burgers’ equation, Results in Physics, 18 (2020), 103231.
آمار
تعداد مشاهده مقاله: 266
تعداد دریافت فایل اصل مقاله: 357


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب