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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,443
تعداد مقالات17,727
تعداد مشاهده مقاله57,889,082
تعداد دریافت فایل اصل مقاله19,512,603
Malge, Shilpa, Lodhi, Ram. (1405). Quintic B-spline method for numerical solution of second-order singularly perturbed delay differential equations. سامانه مدیریت نشریات علمی, 14(1), 36-49. doi: 10.22034/cmde.2024.61474.2650
Shilpa Malge; Ram Kishun Lodhi. "Quintic B-spline method for numerical solution of second-order singularly perturbed delay differential equations". سامانه مدیریت نشریات علمی, 14, 1, 1405, 36-49. doi: 10.22034/cmde.2024.61474.2650
Malge, Shilpa, Lodhi, Ram. (1405). 'Quintic B-spline method for numerical solution of second-order singularly perturbed delay differential equations', سامانه مدیریت نشریات علمی, 14(1), pp. 36-49. doi: 10.22034/cmde.2024.61474.2650
Malge, Shilpa, Lodhi, Ram. Quintic B-spline method for numerical solution of second-order singularly perturbed delay differential equations. سامانه مدیریت نشریات علمی, 1405; 14(1): 36-49. doi: 10.22034/cmde.2024.61474.2650

Quintic B-spline method for numerical solution of second-order singularly perturbed delay differential equations

Computational Methods for Differential Equations
مقاله 4، دوره 14، شماره 1، فروردین 2026، صفحه 36-49    اصل مقاله (455.25 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61474.2650
نویسندگان
Shilpa Malge؛ Ram Kishun Lodhi*
Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India.
چکیده
This article presents a quintic B-spline method to find an approximate solution of the second-order singularly perturbed differential equation in which the convection term occurs with a negative shift. The proposed method gives rise to a pentadiagonal linear system. Thomas' algorithm is employed to solve the obtained system of equations. The method’s convergence is examined through truncation error analysis, and the existence and uniqueness of the solution are also established. Maximum absolute error is tabulated for two numerical examples, proving the proposed method’s efficiency. Graphs are drawn to show the behavior of the solution. A comparative study shows that the obtained solution is better than the previous solutions in the literature. The method is found to be fourth-order convergent. The effect of the delay parameter on the boundary region is also discussed in the example.
کلیدواژه‌ها
Singularly perturbed delay differential equation؛ Boundary value problem؛ Spline methods؛ Quintic B-spline method؛ Existence and uniqueness؛ Uniform mesh؛ Convergence
مراجع
  • [1] A. Bashan, S. B. G. Karakoc, and T. Geyikli, Approximation of the KdVB equation by the quintic B-spline differential quadrature method, Kuwait Journal of Science, 42 (2015), 67–92.
  • [2] R. K. Bawa and S. Natesan, A computational method for self-adjoint singular perturbation problems using quintic spline, Computers and Mathematics with Applications, 50 (2005), 1371–1382.
  • [3] C. M. Bender and S. A. Orszag, Advanced mathematical methods for scientists and engineers, asymptotic methods and perturbation theory, Springer-Verlang, New York, 1999.
  • [4] C. D. Boor, A Practical guide to spline , Springer, New York, 2001.
  • [5] 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.
  • [6] H. G. Debela, S. B. Kejela, and A. D. Negassa, Exponentially fitted numerical method for singularly perturbed differential-difference equations, International Journal of Differential Equations, 2020 (2020), 5768323.
  • [7] A. H. Ejere, G. F. Duressa, M. M. Woldaregay, and T. G. Dinka, An exponentially fitted numerical scheme via domain decomposition for solving singularly perturbed differential equations with large negative shift, Journal of Mathematics, 1 (2022), 7974134.
  • [8] S. Elango, Second order singularly perturbed delay differential equations with non-local boundary condition, Journal of Computational and Applied Mathematics, 417 (2023), 114498.
  • [9] T. S. Eldanaf, M. Elsayed, M. A. Eissa, and F. Ezz-Eldeen Abd Alaal, Quintic B-Spline Method for Solving Sharma Tasso Oliver Equation, Journal of Applied Mathematics and Physics, 10 (2022), 3920–3936.
  • [10] F. Erdogan, An exponentially fitted method for singularly perturbed delay differential equations, ADE-Advances Differential Equations, 2009 (2009), 781579.
  • [11] S. E. Fadugba, J. Vinci Shaalini, O. M. Ogunmiloro, J. T. Okunlola and F. H. Oyelami, Analysis of Exponential–Polynomial Single Step Method for Singularly Perturbed Delay Differential Equations, Journal of Physics: Conference Series, 2199 (2022), 1–14.
  • [12] J. Goh, A. Majid, and A. I. M. Ismail, A quartic B-spline for second-order singular boundary value problems, Computers & Mathematics with Applications, 64 (2012), 115–120.
  • [13] A. Gupta, A. Kaushi Gupta, and A. Kaushik, A higher-order hybrid finite difference method based on grid equidistribution for fourth-order singularly perturbed differential equations, Journal of Applied Mathematics and Computing, 68 (2022), 1163–1191.
  • [14] M. K. Iqbal, M. Abbas, T. Nazir, and N. Ali, Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation, ADE-Advances Differential Equations, 2020 (2020), 1–12.
  • [15] M. K. Kadalbajoo and K. K. Sharma, Numerical analysis of singularly perturbed delay differential equations with layer behavior, Applied Mathematics and Computation, 2157 (2004), 11–28.
  • [16] M. K. Kadalbajoo and K. K. Sharma, ε-uniform fitted mesh method for singularly perturbed differential-difference equations: mixed type of shifts with layer behavior, International Journal of Computer Mathematics, 81 (2004), 49–62.
  • [17] M. K. Kadalbajoo and K. K. Sharma, A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations, Applied Mathematics and Computation, 197 (2008), 692–707.
  • [18] M. K. Kadalbajoo and V. P. Ramesh, Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy, Applied Mathematics and Computation, 188 (2007), 1816–1831.
  • [19] D. Kumar, A uniformly convergent scheme for two-parameter problems having layer behavior, International Journal of Computer Mathematics, Applied Mathematics and Computation, 99 (2022), 553–574.
  • [20] Y. N. Kyrychko and S. J. Hogan, On the Use of Delay Equations in Engineering Applications, Journal of Vibration and Control, Applied Mathematics and Computation, 16 (2010), 943–960.
  • [21] L. B. Liu, C. Zhu, and G. Long, Numerical analysis of a system of semilinear singularly perturbed first-order differential equations on an adaptive grid, Mathematical Methods in the Applied Sciences, 45 (2021), 2042–2057.
  • [22] R. K. Lodhi and H. K. Mishra, Solution of a class of fourth order singular singularly perturbed boundary value problems by quintic B-spline method, Journal of Nigerian Mathematical Society, 35 (2016), 257-265.
  • [23] R. K. Lodhi and H. K. Mishra, Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems, Journal of Computational and Applied Mathematics, 319 (2017) 170–187.
  • [24] R. K. Lodhi and H. K. Mishra, Quintic B-spline method for numerical solution of fourth order singular perturbation boundary value problems, Studia Universitatis Babe¸s-Bolyai Mathematica, 63 (2018), 141–151.
  • [25] R. Mahendran and V. Subburayan, Uniformly convergent finite difference method for reaction-diffusion type third order singularly perturbed delay differential equation, Turkish Journal of Mathematics, 46 (2022), 360–376.
  • [26] R. E. J. O’Malley, Introduction to Singular Perturbation, Academic Press, New York, 1974.
  • [27] M. Prenter, Splines and Variational Methods, John Wiley & Sons, Inc. 1975.
  • [28] A. S. V. Ravi Kanth and P. M. M. Kumar, Computational results and analysis for a class of linear and nonlinear singularly perturbed convection delay problems on Shishkin mesh, Hacettepe Journal of Mathematics and Statistics, 49 (2020), 221–235.
  • [29] P. Roul and K. Thula, A fourth-order B-spline collocation method and its error analysis for Bratu-type and Lane–Emden problems, International Journal of Computational Mathematics, 96 (2019), 85–104.
  • [30] A. Saeedi, conditions, Engineering with Computers, Engineering with Computers, 33 (2017), 335–348.
  • [31] R. P. Singh and Y. N. Reddy, A fitted method for singularly perturbed differential-difference equations having boundary layer via deviating argument and interpolation, Journal of Mathematical and Computational Science, 32 (2020), 2467–2492.
  • [32] A. S. Singh and D. Kumar, Spline-based parameter-uniform scheme for fourth-order singularly perturbed differential equations, Journal of Mathematical Chemistry, 60 (2022), 1872–1902.
  • [33] N. Senu, K. C. Lee, A. Ahmadian, and S. N. I. Ibrahim, Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation, Alexandria Engineering Journal, 61 (2022), 5819–5835.
  • [34] M. M. Woldaregay, H. G. Debela, and G. F. Duressa, Uniformly convergent fitted operator method for singularly perturbed delay differential equations, Computational Methods for Differential Equations, 10 (2022), 502–518.
آمار
تعداد مشاهده مقاله: 214
تعداد دریافت فایل اصل مقاله: 380


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب