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

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Lubo, Gemeda Tolessa, Duressa, Gemechis File. (1401). Linear B-spline finite element Method for solving delay reaction diffusion equation. سامانه مدیریت نشریات علمی, 11(1), 161-174. doi: 10.22034/cmde.2022.49678.2066
Gemeda Tolessa Lubo; Gemechis File Duressa. "Linear B-spline finite element Method for solving delay reaction diffusion equation". سامانه مدیریت نشریات علمی, 11, 1, 1401, 161-174. doi: 10.22034/cmde.2022.49678.2066
Lubo, Gemeda Tolessa, Duressa, Gemechis File. (1401). 'Linear B-spline finite element Method for solving delay reaction diffusion equation', سامانه مدیریت نشریات علمی, 11(1), pp. 161-174. doi: 10.22034/cmde.2022.49678.2066
Lubo, Gemeda Tolessa, Duressa, Gemechis File. Linear B-spline finite element Method for solving delay reaction diffusion equation. سامانه مدیریت نشریات علمی, 1401; 11(1): 161-174. doi: 10.22034/cmde.2022.49678.2066

Linear B-spline finite element Method for solving delay reaction diffusion equation

Computational Methods for Differential Equations
مقاله 12، دوره 11، شماره 1، فروردین 2023، صفحه 161-174    اصل مقاله (764.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.49678.2066
نویسندگان
Gemeda Tolessa Lubo* 1؛ Gemechis File Duressa2
1Department of Mathematics‎, ‎Wollega University‎, ‎Nekemte‎, ‎Ethiopia.
2Department of Mathematics‎, ‎Jimma University‎, ‎Jimma‎, ‎Ethiopia.
چکیده
This paper is concerned with the numerical treatment of delay reaction-diffusion with the Dirichlet boundary condition. The finite element method with linear B-spline basis functions is utilized to discretize the space variable. The Crank-Nicolson method is used for the processes of time discretization. Sufficient and necessary conditions for the numerical method to be asymptotically stable are investigated. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method. 
کلیدواژه‌ها
Delay reaction diffusion equation؛ Crank Nicolson؛ Linear B-spline؛ Finite element method؛ Asymtotic stability؛ Convergence
مراجع
  • [1] A. M. A. Adam, E. B. M. Bashier, M. H. A. Hashim, and K. C. Patidar, Fitted Galerkin spectral method to solve delay partial differential equations, Math. Methods Appl. Sci., 39 (2016), 3102–3115.
  • [2] T. Ak, S. Dhawan, S. B. Karakoc, S. K. Bhowmik, and K. R. Raslan, Numerical study of Rosenau -KdV equation using finite element method based on collocation approach, Math. Model. Anal., 22 (2017), 373–388.
  • [3] E. N. Aksan and A. Ozde, Numerical solution of Korteweg -de Vries equation by Galerkin B-spline finite element method, Appl. Math. Comput., 175 (2006), 1256–1265.
  • [4] E. N. Aksan, An application of cubic B-Spline finite element method for the Burgers equation, Therm Sci., 22 (2018), 195–202.
  • [5] I. Aziz and R. Amin, Numerical solution of a class of delay differential and delay partial differential equations via Haar wavelet, Appl. Math. Model., 40 (2016), 10286–10299.
  • [6] S. K. Bhowmik and S. B. Karakoc, Numerical solutions of the generalized equal width wave equation using the Petrov -Galerkin method, Appl. Anal., 100 (2021), 714–734.
  • [7] A. H. Bhrawy, M. A. Abdelkawy, and F. Mallawi, An accurate Chebyshev pseudospectral scheme for multi- dimensional parabolic problems with time delays, Boundary Value Problems, (2015), 1–20.
  • [8] H. Brunner, Collocation methods for Volterra integral and related functional differential equations, Cambridge university press, 2004.
  • [9] X. Chen and L. Wang, The variational iteration method for solving a neutral functional-differential equation with proportional delays, Comput. Math. with Appl., 59 (2010), 2696–2702.
  • [10] I. Dag, B. Saka, and D. Irk, Galerkin method for the numerical solution of the RLW equation using quintic B-splines, J. Comput. Appl. Math., 190 (2006), 532–547.
  • [11] S. Dhawan, S. K. Bhowmik, and S. Kumar, Galerkin-least square B-spline approach toward advection-diffusion equation, Appl. Math. Comput., 261 (2015), 128–140.
  • [12] N. Habibi and A. Mesforush, Extending a new two -grid waveform relaxation on a spatial finite element discretiza- tion, Comput. methods differ. equ., 9 (2021), 1148–1162.
  • [13] N. Habibi, A. Mesforush, F. J. Gaspar, and C. Rodrigo, Semi -algebraic mode analysis for finite element discreti- sations of the heat equation, Comput. methods differ. equ., 9 (2021), 146–158.
  • [14] C. Huang and S. Vandewalle, Unconditionally stable difference methods for delay partial differential equations, Numerische Mathematik, 122 (2012), 579–5601.
  • [15] Z. Jackiewicz and B. Zubik-Kowal, Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations, Appl. Numer. Math., 56 (2006), 433–443.
  • [16] S. Kutluay and Y. Ucar, Numerical solutions of the coupled Burgers? equation by the Galerkin quadratic B-spline finite element method, Math. Methods Appl. Sci., 36 (2013), 2403–2415.
  • [17] M. Lakestani, Numerical solutions of the KdV equation using B -spline functions, Iran J. Sci. Technol. Trans. A. Sci ., 41 (2017), 409–417.
  • [18] M. Lakestani and M. Dehghan, Numerical solution of Fokker -Planck equation using the cubic B -spline scaling functions, Numer. Methods Partial Differ. Equ., 25 (2009), 418–429.
  • [19] D. Li, C. Zhang, and H. Qin, LDG method for reaction-diffusion dynamical systems with time delay, Appl. Math. Comput., 217 (2011), 9173–9181.
  • [20] D. Li, C. Zhang, and J. Wen, A note on compact finite difference method for reaction -diffusion equations with delay, Appl. Math. Model., 39 (2015), 1749–1754.
  • [21] D. Li and C. Zhang, On the long time simulation of reaction -diffusion equations with delay, Sci. World J., (2014), 2014.
  • [22] H. Liang, Convergence and asymptotic stability of Galerkin methods for linear parabolic equations with delays, Appl. Math. Comput., 264 (2015), 160–178.
  • [23] T. Ozis, A. Esen, and S. Kutluay, Numerical solution of Burgers? equation by quadratic B-spline finite elements, Appl. Math. Comput., 165 (2005), 237–249.
  • [24] A. Rachid, M. Bahaj, and R. Fakhar, Finite volume element approximation for time dependent convection diffusion reaction equations with memory, Comput. methods differ. equ., 9 (2021), 977–1000.
  • [25] E. Reyes, F. Rodriguez, and J. A. Martin, Analytic -numerical solutions of diffusion mathematical models with delays, Comput. Math. with Appl., 56 (2008), 743–753.
  • [26] F. A. Rihan, Computational methods for delay parabolic and time -fractional partial differential equations, Numer. Methods Partial Differ. Equ., 26 (2010), 1556-1571.
  • [27] B. Saka and I. Dag, Quartic B-spline collocation algorithms for numerical solution of the RLW equation, Numer. Methods Partial Differ. Equ., 23 (2007), 731–751.
  • [28] M. Sana and M. Mustahsan, Finite element approximation of optimal control problem with weighted extended B-splines, Math., 7 (2019), 452.
  • [29] A. A. Soliman, A Galerkin solution for Burgers’ equation using cubic B-spline finite elements, Abstr. Appl. Anal., 2012 (2012), Hindawi.
  • [30] Z. Sun and Z. Zhang, A linearized compact difference scheme for a class of nonlinear delay partial differential equations, Appl. Math. Model., 37 (2013), 742–752.
  • [31] V. Thomee, Galerkin finite element methods for parabolic problems, Springer Science & Business Media, 2007.
  • [32] H. Tian, Asymptotic stability analysis of the linear θ -method for linear parabolic differential equations with delay, J. Differ. Equ. Appl., 15 (2009), 473–487.
  • [33] H. Tian, D. Zhang, and Y. Sun, Delay -independent stability of Euler method for nonlinear one -dimensional diffusion equation with constant delay, Frontiers of Mathematics in China, 4 (2009), 169–179.
  • [34] S. Vandewalle and M. J. Gander, Optimized overlapping Schwarz methods for parabolic PDEs with time-delay, In Domain Decomposition Methods in Science and Engineering, 2005, 291–298.
  • [35] S. Wu and S. Gan, Analytical and numerical stability of neutral delay integro-differential equations and neutral delay partial differential equations, Comput. Math. with Appl, 55 (2008), 2426–2443.
  • [36] S. L. Wu, C. M. Huang, and T. Z. Huang, Convergence analysis of the overlapping Schwarz waveform relaxation algorithm for reaction-diffusion equations with time delay, IMA J. Numer. Anal., 32 (2012), 632–671.
  • [37] J. Wu and X. Zhang, Finite element method by using quartic B-splines, Numer. Methods Partial Differ. Equ., 27 (2011), 818–828.
  • [38] S. I. Zaki, A quintic B-spline finite elements scheme for the KdV equation, Comput. Methods Appl. Mech. Eng., 188 (2000), 121–134.
  • [39] Q. Zhang and C. Zhang, A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations, Appl. Math. Lett., 26 (2013), 306–312.
  • [40] B. Zubik-Kowal, Stability in the numerical solution of linear parabolic equations with a delay term, BIT Numerical Mathematics, 41 ( 2001), 191–206.
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