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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,538
تعداد مقالات18,760
تعداد مشاهده مقاله62,627,298
تعداد دریافت فایل اصل مقاله22,585,828
Azad, Amirreza, Yaghoubi, Ehsan, Jafari, Azadeh. (1403). Numerical solution of Burgers' equation with nonlocal boundary condition: Use of Keller-Box scheme. سامانه مدیریت نشریات علمی, 12(3), 425-437. doi: 10.22034/cmde.2023.54380.2271
Amirreza Azad; Ehsan Yaghoubi; Azadeh Jafari. "Numerical solution of Burgers' equation with nonlocal boundary condition: Use of Keller-Box scheme". سامانه مدیریت نشریات علمی, 12, 3, 1403, 425-437. doi: 10.22034/cmde.2023.54380.2271
Azad, Amirreza, Yaghoubi, Ehsan, Jafari, Azadeh. (1403). 'Numerical solution of Burgers' equation with nonlocal boundary condition: Use of Keller-Box scheme', سامانه مدیریت نشریات علمی, 12(3), pp. 425-437. doi: 10.22034/cmde.2023.54380.2271
Azad, Amirreza, Yaghoubi, Ehsan, Jafari, Azadeh. Numerical solution of Burgers' equation with nonlocal boundary condition: Use of Keller-Box scheme. سامانه مدیریت نشریات علمی, 1403; 12(3): 425-437. doi: 10.22034/cmde.2023.54380.2271

Numerical solution of Burgers' equation with nonlocal boundary condition: Use of Keller-Box scheme

Computational Methods for Differential Equations
مقاله 1، دوره 12، شماره 3، مهر 2024، صفحه 425-437    اصل مقاله (566.93 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.54380.2271
نویسندگان
Amirreza Azad1، 2؛ Ehsan Yaghoubi1؛ Azadeh Jafari* 1
1School of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran.
2Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canada.
چکیده
In this paper, we transform the given nonlocal boundary condition problem into a manageable local equation. By introducing an additional transformation of the variables, we can simplify this equation into conformable Burgers’ equation. Thus, the Keller Box method is used as a numerical scheme to solve the equation. A comparison is made between numerical results and the analytic solution to validate the results of our proposed method.
کلیدواژه‌ها
Nonlocal boundary condition؛ Burgers’ Equation؛ Keller-Box scheme
مراجع
  • [1] N. Al-Zaid and H. Bakodah, Iterative algorithm for parabolic and hyperbolic pdes with nonlocal boundary conditions, Journal of Ocean Engineering and Science, 3(4) (2018), 316–324.
  • [2] E. Ashpazzadeh, B. Han, and M. Lakestani, Biorthogonal multiwavelets on the interval for numerical solutions of burgers’ equation, Journal of Computational and Applied Mathematics, 317 (2017), 510–534.
  • [3] J. Bec and K. Khanin, Burgers turbulence, Physics reports, 447(1-2) (2007), 1–66.
  •  4] G. Berikelashvili and N. Khomeriki, On a numerical solution of one nonlocal boundary-value problem with mixed dirichlet–neumann conditions, Lithuanian Mathematical Journal, 53 (2013), 367–380.
  • [5] J. Biazar, Z. Ayati, and S. Shahbazi, Solution of the burgers equation by the method of lines, American Journal of Numerical Analysis, 2(1) (2014) 1–3.
  • [6] M. P. Bonkile, A. Awasthi, C. Lakshmi, V. Mukundan, and V. Aswin, A systematic literature review of burgers’ equation with recent advances, Pramana, 90 (2018), 1–21.
  • [7] A. Borhanifar, S. Shahmorad, and E. Feizi, A matrix formulated algorithm for solving parabolic equations with nonlocal boundary conditions, Numerical Algorithms, 74 (2017), 1203–1221.
  • [8] A. Bouziani, N. Merazga, and S. Benamira, Galerkin method applied to a parabolic evolution problem with nonlocal boundary conditions, Nonlinear Analysis: Theory, Methods & Applications, 69(5-6) (2008), 1515–1524.
  • [9] J. R. Cannon, The solution of the heat equation subject to the specification of energy, Quarterly of Applied Mathematics, 2(2) (1963), 155–160.
  • [10] M. Dehghan, Numerical solution of a non-local boundary value problem with neumann’s boundary conditions, Communications in numerical methods in engineering, 19(1) (2003), 1–12.
  • [11] M. Dehghan, On the solution of an initial-boundary value problem that combines neumann and integral condition for the wave equation, Numerical Methods for Partial Differential Equations: An International Journal, 21(1) (2005), 24–40.
  • [12] I. A. Ganaie and V. Kukreja, Numerical solution of burgers’ equation by cubic hermite collocation method, Applied Mathematics and Computation, 237 (2014), 571–581.
  • [13] K. Goyal and M. Mehra, A fast adaptive diffusion wavelet method for burger’s equation, Computers & Mathematics with Applications, 68(4) (2014), 568–577.
  • [14] Y. Guo, Y.-f. Shi, and Y.-m. Li, A fifth-order finite volume weighted compact scheme for solving one-dimensional burgers’ equation, Applied Mathematics and Computation, 281 (2016) 172–185.
  • [15] B. Inan and A. R. Bahadir, Numerical solution of the one-dimensional burgers’ equation: Implicit and fully implicit exponential finite difference methods, Pramana, 81 (2013), 547–556.
  • [16] Z. Iqbal, E. Azhar, Z. Mehmood, and E. Maraj, Melting heat transport of nanofluidic problem over a riga plate with erratic thickness: Use of keller box scheme, Results in physics, 7 (2017) 3648–3658.
  • [17] S. u. Islam, I. Aziz, and M. Ahmad, Numerical solution of two-dimensional elliptic pdes with nonlocal boundary conditions, Computers & Mathematics with Applications, 69(3) (2015), 180–205.
  • [18] M. Javidi. A numerical solution of burger’s equation based on modified extended bdf scheme, International Mathematical Forum, 1 (2006), pages 1565–1570.
  • [19] N. Jha and S. Verma, Infinitely smooth multiquadric rbfs combined high-resolution compact discretization for nonlinear 2d elliptic pdes on a scattered grid network, Computational Methods for Differential Equations, 11(4) (2023), 753–775.
  • [20] R. Kannan and Z. Wang, A high order spectral volume solution to the burgers’ equation using the hopf–cole transformation, International journal for numerical methods in fluids, 69(4) (2012), 781–801.
  • [21] M. Kumar and S. Pandit, A composite numerical scheme for the numerical simulation of coupled burgers’ equation, Computer Physics Communications, 185(3) (2014) 809–817.
  • [22] Y. Lin, Parabolic partial differential equations subject to nonlocal boundary conditions, 1988. thesis (Ph.D.)– Washington State University.
  • [23] J. Martin-Vaquero and J. Vigo-Aguiar, On the numerical solution of the heat conduction equations subject to nonlocal conditions, Applied Numerical Mathematics, 59(10) (2009), 2507–2514.
  • [24] S. Mesloub, On a singular two dimensional nonlinear evolution equation with nonlocal conditions, Nonlinear Analysis: Theory, methods & applications, 68(9) (2008), 2594–2607.
  • [25] S. Mesloub and S. A. Messaoudi, A nonlocal mixed semilinear problem for second-order hyperbolic equations Electronic Journal of Differential Equations, 30 (2003), 1–17.
  • [26] R. Mittal and R. Jain, Numerical solutions of nonlinear burgers’ equation with modified cubic b-splines collocation method, Applied Mathematics and Computation, 218(15) (2012), 7839–7855.
  • [27] R. Mittal, H. Kaur, and V. Mishra, Haar wavelet-based numerical investigation of coupled viscous burgers’ equation International Journal of Computer Mathematics, 92(8) (2015), 1643–1659.
  • [28] B. Nemati Saray, M. Lakestani, and M. Dehghan, On the sparse multiscale representation of 2-d burgers equations by an efficient algorithm based on multiwavelets, Numerical Methods for Partial Differential Equations, 39(3) (2023), 1938–1961.
  • [29] B. M. Prakash, A. Awasthi, and S. Jayaraj, A numerical simulation based on modified keller box scheme for fluid flow: The unsteady viscous burgers’ equation, Mathematical Analysis and its Applications, Springer Proceedings in Mathematics & Statistics, 143 (2015), 565–575.
  • [30] L. S. Pulkina, A nonlocal problem with integral conditions for a hyperbolic equation, Differentsial’nye Uravneniya, 40(7) (2004) 887–892.
  • [31] M. Ramezani, M. Dehghan, and M. Razzaghi, Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition, Numerical Methods for Partial Differential Equations: An International Journal, 24(1) (2008), 1–8.
  • [32] S. Sajaviˇcus, Radial basis function method for a multidimensional linear elliptic equation with nonlocal boundary conditions, Computers & Mathematics with Applications, 67(7) (2014), 1407–1420.
  • [33] M. Siddique. Smoothing of crank–nicolson scheme for the two-dimensional diffusion with an integral condition, Applied mathematics and computation, 214(2) (2009), 512–522.
  • [34] L. Ta-Tsien, A class of non-local boundary value problems for partial differential equations and its applications in numerical analysis, Journal of computational and applied mathematics, 28 (1989), 49–62.
  • [35] M. Vynnycky and S. Mitchell, On the accuracy of a finite-difference method for parabolic partial differential equations with discontinuous boundary conditions, Numerical Heat Transfer, Part B: Fundamentals, 64(4) (2013) 275–292.
  • [36] G. Zhao, X. Yu, and R. Zhang, The new numerical method for solving the system of two-dimensional burgers’ equations, Computers & Mathematics with Applications, 62(8) (2011) 3279–3291, 2011.
  • [37] R. Zolfaghari and A. Shidfar, Solving a parabolic pde with nonlocal boundary conditions using the sinc method, Numerical Algorithms, 62 (2013), 411–427.
آمار
تعداد مشاهده مقاله: 915
تعداد دریافت فایل اصل مقاله: 1,420


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب