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Regal, Akhila, Kumar S, Dinesh. (1403). Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition. سامانه مدیریت نشریات علمی, 13(2), 618-633. doi: 10.22034/cmde.2024.58538.2477
Akhila Mariya Regal; Dinesh Kumar S. "Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition". سامانه مدیریت نشریات علمی, 13, 2, 1403, 618-633. doi: 10.22034/cmde.2024.58538.2477
Regal, Akhila, Kumar S, Dinesh. (1403). 'Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition', سامانه مدیریت نشریات علمی, 13(2), pp. 618-633. doi: 10.22034/cmde.2024.58538.2477
Regal, Akhila, Kumar S, Dinesh. Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition. سامانه مدیریت نشریات علمی, 1403; 13(2): 618-633. doi: 10.22034/cmde.2024.58538.2477

Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition

Computational Methods for Differential Equations
مقاله 19، دوره 13، شماره 2، خرداد 2025، صفحه 618-633    اصل مقاله (409.38 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.58538.2477
نویسندگان
Akhila Mariya Regal؛ Dinesh Kumar S*
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India.
چکیده
The cubic spline in tension method is taken into consideration to solve the singularly perturbed delay differential equations of convection diffusion type with integral boundary condition. Simpson’s 1/3 rule is used to the non-local boundary condition and three model problems are examined for numerical treatment and are addressed using a variety of values for the perturbation parameter  and the mesh size to verify the scheme’s applicability. The computational results and rate of convergence are given in tables, and it is seen that the proposed method is more precise and improves the methods used in the literature. 
کلیدواژه‌ها
Singular perturbation problems؛ Delay differential equations؛ Cubic spline in tension؛ Integral boundary conditions
مراجع
  • [1] P. P. Chakravarthy, S. D. Kumar, and R. N. Rao, Numerical solution of second order singularly perturbed delay differential equations via cubic spline in tension, International Journal of Applied and Computational Mathematics, 3 (2017), 1703-1717.
  • [2] R. V. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of CD4+ T-cells, Mathematical Biosciences, 165(1) (2000), 27-39.
  • [3] I. T. Daba and G. F. Duressa, A Robust computational method for singularly perturbed delay parabolic convectiondiffusion equations arising in the modeling of neuronal variability, Computational Methods for Differential Equations, 10(2) (2022), 475-488.
  • [4] H. G. Debela and G. F. Duressa, Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition, Journal of the Egyptian Mathematical Society, 28 (2020), 1-16.
  • [5] H. G. Debela and G. F. Duressa, Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition, International Journal of Engineering and Applied Sciences, 11(4) (2019), 476-493.
  • [6] H. G. Debela and G. F. Duressa, Fitted non-polynomial spline method for singularly perturbed differential difference equations with integral boundary condition, Journal of Applied and Engineering Mathematics, 12(4) (2022), 12131227.
  • [7] G. F. Duressa and M. M. Woldaregay, Fitted numerical scheme for solving singularly perturbed parabolic delay partial differential equations, Tamkang Journal of Mathematics, 53(4) (2022), 345-362.
  • [8] F. Erdogan and Z. Cen, A uniformly almost second order convergent numerical method for singularly perturbed delay differential equations, Journal of Computational and Applied Mathematics, 333 (2018), 382-394.
  • [9] S. Erdur and C. Tunc, On the existence of periodic solutions of third order delay differential equations, Computational Methods for Differential Equations, 11(2) (2023), 319-331.
  • [10] G. File, G. Gadisa, T. Aga, and Y. N. Reddy, Numerical solution of singularly perturbed delay reaction-diffusion equations with layer or oscillatory behaviour, American Journal of Numerical Analysis, 5(1) (2017), 1-10.
  • [11] V. Glizer, Asymptotic analysis and solution of a finite-horizon H∞ control problem for singularly-perturbed linear systems with small state delay, Journal of Optimization Theory and Applications, 117 (2003), 295-325.
  • [12] M. K. Kadalbajoo and D. Kumar, Fitted mesh B-spline collocation method for singularly perturbed differentialdifference equations with small delay, Applied Mathematics and Computation, 204(1) (2008), 90-98.
  • [13] M. K. Kadalbajoo and K. K. Sharma, Numerical analysis of boundary-value problems for singularly-perturbed differential-difference equations with small shifts of mixed type, Journal of Optimization theory and Applications, 115 (2002), 145-163.
  • [14] M. K. Kadalbajoo and K. K. Sharma, Numerical treatment of boundary value problems for second order singularly perturbed delay differential equations, Computational and Applied Mathematics, 24 (2005), 151-172.
  • [15] G. G. Kiltu, G. F. Duressa, and T. A. Bullo, Numerical treatment of singularly perturbed delay reaction-diffusion equations, International Journal of Engineering, Science and Technology, 12(1) (2020), 15-24.
  • [16] K. Kumar, P. P. Chakravarthy, H. Ramos, and J. Vigo-Aguiar, A stable finite difference scheme and error estimates for parabolic singularly perturbed pdes with shift parameters, Journal of Computational and Applied Mathematics, 405 (2022), 113050.
  • [17] D. Kumar and P. Kumari, A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition, Journal of Applied Mathematics and Computing, 63(1) (2020), 813-828.
  • [18] D. Kumar and P. Kumari, Parameter-uniform numerical treatment of singularly perturbed initial-boundary value problems with large delay, Applied Numerical Mathematics, 153 (2020), 412-429.
  • [19] N. S. Kumar and R. N. Rao, A second order stabilized central difference method for singularly perturbed differential equations with a large negative shift, Differential Equations and Dynamical Systems, 31 (2020), 1-18.
  • [20] M. Lalu, K. Phaneendra, and S. P. Emineni, Numerical approach for differential-difference equations having layer behaviour with small or large delay using non-polynomial spline, Soft Computing, 25(21) (2021), 13709-13722.
  • [21] H. Li and F. Sun, Existence of solutions for integral boundary value problems of second-order ordinary differential equations, Boundary Value Problems, 2012 (2012), 1-7.
  • [22] S. Nicaise and C. Xenophontos, Robust approximation of singularly perturbed delay differential equations by the hp finite element method, Computational Methods in Applied Mathematics, 13(1) (2013), 21-37.
  • [23] K. C. Patidar and K. K. Sharma, Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance, International Journal for Numerical Methods in Engineering, 66(2) (2006), 272-296.
  • [24] E. Sekar and A. Tamilselvan, Singularly perturbed delay differential equations of convection–diffusion type with integral boundary condition, Journal of Applied Mathematics and Computing, 59 (2019), 701-722.
  • [25] P. A. Selvi and N. Ramanujam, An iterative numerical method for singularly perturbed reaction–diffusion equations with negative shift, Journal of Computational and Applied Mathematics, 296 (2016), 10-23.
  • [26] K. K. Sharma, Parameter-uniform fitted mesh method for singularly perturbed delay differential equations with layer behavior, Electronic Transactions on Numerical Analysis, 23 (2006), 180-201.
  • [27] A. Sharma and P. Rai, A hybrid numerical scheme for singular perturbation delay problems with integral boundary condition, Journal of Applied Mathematics and Computing, 68(5) (2022), 3445-3472.
  • [28] V. Subburayan and N. Ramanujam, An initial value technique for singularly perturbed convection–diffusion problems with a negative shift, Journal of Optimization Theory and Applications, 158 (2013), 234-250.
  • [29] S. K. Tesfaye, M. M. Woldaregay, T. G. Dinka, and G. F. Duressa, Fitted computational method for solving singularly perturbed small time lag problem, BMC Research Notes, 15(1) (2022), 318.
  • [30] D. Y. Tzou, Macro-to microscale heat transfer: the lagging behavior, John Wiley and Sons, 2014.
 

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