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Wondimu, Getu Mekonnen, Dinka, Tekle Gemechu, Woldaregay, Mesfin, Duressa, Gemechis File. (1402). Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition. سامانه مدیریت نشریات علمی, 11(3), 478-494. doi: 10.22034/cmde.2023.49239.2054
Getu Mekonnen Wondimu; Tekle Gemechu Dinka; Mesfin Woldaregay; Gemechis File Duressa. "Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition". سامانه مدیریت نشریات علمی, 11, 3, 1402, 478-494. doi: 10.22034/cmde.2023.49239.2054
Wondimu, Getu Mekonnen, Dinka, Tekle Gemechu, Woldaregay, Mesfin, Duressa, Gemechis File. (1402). 'Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition', سامانه مدیریت نشریات علمی, 11(3), pp. 478-494. doi: 10.22034/cmde.2023.49239.2054
Wondimu, Getu Mekonnen, Dinka, Tekle Gemechu, Woldaregay, Mesfin, Duressa, Gemechis File. Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition. سامانه مدیریت نشریات علمی, 1402; 11(3): 478-494. doi: 10.22034/cmde.2023.49239.2054

Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition

Computational Methods for Differential Equations
مقاله 4، دوره 11، شماره 3، شهریور 2023، صفحه 478-494    اصل مقاله (755.12 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.49239.2054
نویسندگان
Getu Mekonnen Wondimu1؛ Tekle Gemechu Dinka1؛ Mesfin Woldaregay* 1؛ Gemechis File Duressa2
1Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia.
2Department of Mathematics, Jimma University, Jimma, Ethiopia.
چکیده
This article presents a numerical treatment of the singularly perturbed delay reaction diffusion problem with an integral boundary condition. In the considered problem, a small parameter ", is multiplied on the higher order derivative term. The presence of this parameter causes the existence of boundary layers in the solution. The solution also exhibits an interior layer because of the large spatial delay. Simpson's 1/3 rule is applied to approximate the integral boundary condition given on the right end plane. A standard finite difference scheme on piecewise uniform Shishkin mesh is proposed to discretize the problem in the spatial direction, and the Crank-Nicolson method is used in the temporal direction. The developed numerical scheme is parameter uniformly convergent, with nearly two orders of convergence in space and two orders of convergence in time. Two numerical examples are considered to validate the theoretical results.
کلیدواژه‌ها
Singularly perturbed problems؛ Fitted mesh scheme؛ Integral boundary condition
مراجع
  • [1] G. M. Amiraliyev, I. G. Amiraliyeva, and K. Mustafa, A numerical treatment for singularly perturbed differential equations with integral boundary condition, Appl. Math. Comput., 185 (2007), 574–582.
  • [2] A. R. Ansari, S. A. Bakr, and G. I. Shishkin, A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations, J. Comput. Appl. Math., 205 (2007), 552–566.
  • [3] E. BM. Bashier and K. C. Patidar, A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation, Appl. Math. Comput., 217 (2011), 4728–4739.
  • [4] A. Das and S. Natesan, Second-order uniformly convergent numerical method for singularly perturbed delay par- abolic partial differential equations, Int. J. Comput. Math, 95(2018), 490–510.
  • [5] H. G. Debela and G. F. Duressa, Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition, Int. j. eng. appl. sci., 11 (2019), 476–493.
  • [6] H .G. Debela and G. F. Duressa, Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition, J. Egyptian Math. Soc., em 28 (2020), 1–16.
  • [7] H. G. Debela and G. F. Duressa, Uniformly convergent numerical method for singularly perturbed convection- diffusion type problems with nonlocal boundary condition, Int J Numer Methods Fluids, 92 (2020), 1914–1926.
  • [8] H. G. Debela and G. F. Duressa, Fitted operator finite difference method for singularly perturbed differential equations with integral boundary condition, Kragujev. J. Math., 47 (2023), 637–651.
  • [9] W. T. Gobena and G. F. Duressa, Parameter uniform numerical methods for singularly perturbed delay parabolic differential equations with non-local boundary condition, Int. J. Eng. Sci. Technol., 13 (2021), 57-71.
  • [10] W. T. Gobena and G. F. Duressa, Fitted operator average finite difference method for singularly perturbed delay parabolic reaction diffusion problems with non-local boundary conditions, Tamkang J. Math., (2022).
  • [11] L. Govindarao and J. Mohapatra, Numerical analysis and simulation of delay parabolic partial differential equation involving a small parameter, Engrg. Comput., 37 (2019), 289-312.
  • [12] L. Govindarao, J. Mohapatra, and A. Das, A fourth-order numerical scheme for singularly perturbed delay para- bolic problem arising in population dynamics, J. Appl. Math. Comput., 63 (2020), 171–195.
  • [13] W. S. Hailu and G. F. Duressa, Parameter-uniform cubic spline method for singularly perturbed parabolic differ- ential equation with large negative shift and integral boundary condition, Res. Math., 9 (2022), 2151080.
  • [14] D. Kumar and P. Kumari, A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition, J. Appl. Math. Comput., 63(2020), 813–828.
  • [15] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. UralCeva, Linear and quasilinear equations of parabolic type, translations of mathematical monographs, Amer. Math. Soc. ( N.S. ), 23(1968), Providence RI, (1968).
  • [16] M. Manikandan, N. Shivaranjani, J. J. H. Miller, and S. Valarmathi, A  parameter-uniform  numerical  method  for  a boundary value problem for a singularly perturbed delay differential equation, Adv. Appl. Math., Springer, 2014 (2014), 71–88.
  • [17] J. J. H. Miller, E. ORiordan, G. I. Shishkin, and L. P. Shishkina, Fitted mesh methods for problems with parabolic boundary layers, In Mathematical Proceedings of the Royal Irish Academy, JSTOR, (1998), 173–190.
  • [18] E. Sekar and A. Tamilselvan, Finite difference scheme for third order singularly perturbed delay differential equa- tion of convection diffusion type with integral boundary condition, J. Appl. Math. Comput., 61 (3019), 72–86.
  • [19] E. Sekar and A. Tamilselvan, Finite difference scheme for singularly perturbed system of delay differential equations with integral boundary conditions, J-KSIAM., 22 (2018), 201–215.
  • [20] E. Sekar and A. Tamilselvan, Singularly perturbed delay differential equations of convectiondiffusion type with integral boundary condition, J. Appl. Math. Comput., 9 (2019), 701–722.
  • [21] E. Sekar and A. Tamilselvan, Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition, J. Appl. Math. Comput. Mech., 18 (2019), 99-110.
  • [22] E. Sekar, A. Tamilselvan, R. Vadivel,  N.  Gunasekaran,  H.  Zhu,  J.  Cao,  and  X.  Li,  Finite  difference  scheme  for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition, Adv. Difference Equ.,151 (2021), 1-20.
  • [23] P. A. Selvi and N. Ramanujam, A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with robin type boundary condition, Appl. Math. Comput., 296 (2017), 101–115.
  • [24] G. I. Shishkin, Approximation of the solutions of singularly perturbed boundary-value problems with a parabolic boundary layer. USSR, Comput. Math. Math. Phys., 29 (1989), 1–10.
  • [25] M. M. Woldaregay, W. T. Aniley, and G. F. Duressa, Novel numerical scheme for singularly perturbed time delay convection-diffusion equation, Adv. Math. Phys., 2021 (2021).
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