Non-polynomial spline approach for solving system of singularly perturbed delay differential equations of large delay

References

• Chakravarthy PP, Gupta T. 2020. Numerical solution of a weakly coupled system of singularly perturbed delay differential equations via cubic spline in tension. Natl Acad Sci Lett. 43:259–262. doi: 10.1007/s40009-019-00806-0.
   Web of Science ®Google Scholar
• Chakravarthy PP, Kumar K. 2021. A novel method for singularly perturbed delay differential equations of reaction-diffusion type. Differ Equ Dyn Syst. 29(3):723–734. doi: 10.1007/s12591-017-0399-x.
   Web of Science ®Google Scholar
• Chen Y, Wu J. 2001. The asymptotic shapes of periodic solutions of a singular delay differential system. J Differ Equ. 169(2):614–632. doi: 10.1006/jdeq.2000.3910.
   Web of Science ®Google Scholar
• Culshaw RV, Ruan S. 2000. A delay-differential equation model of HIV infection of CD4+ T-cells. Math Biosci. 165(1):27–39. doi: 10.1016/S0025-5564(00)00006-7.
   PubMed Web of Science ®Google Scholar
• Erdogan F, Sakar MG, Saldır O. 2020. A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Appl Math & Nonlin Sci. 5(1):425–436. doi: 10.2478/amns.2020.1.00040.
   Google Scholar
• Glizer VY. 2000. Asymptotic solution of a boundary-value problem for linear singularly-perturbed functional differential equations arising in optimal control theory. J Optim Theory Appl. 106(2):309–335. doi: 10.1023/A:1004651430364.
   Web of Science ®Google Scholar
• Gourley SA, Kuang Y. 2004. A stage structured predator-prey model and its dependence on maturation delay and death rate. J Math Biol. 49(2):188–200. doi: 10.1007/s00285-004-0278-2.
   PubMed Web of Science ®Google Scholar
• Kot M. 2001. Elements of mathematical ecology. Cambridge, United Kingdom: Cambridge University Press.
   Google Scholar
• Kuang Y. 1993. Delay differential equations: with applications in population dynamics. Cambridge, Massachusetts, United States: Academic press.
   Google Scholar
• Lange CG, Miura RM. 1982. Singular perturbation analysis of boundary value problems for differential-difference equations. SIAM J Appl Math. 42(3):502–531. doi: 10.1137/0142036.
   Web of Science ®Google Scholar
• Lange CG, Miura RM. 1994. Singular perturbation analysis of boundary-value problems for differential-difference equations. VI. Small shifts with rapid oscillations. SIAM J Appl Math. 54(1):273–283. doi: 10.1137/S0036139992228119.
   Web of Science ®Google Scholar
• Longtin A, Milton JG. 1988. Complex oscillations in the human pupil light reflex with mixed and delayed feedback. Math Biosci. 90(1–2):183–199. doi: 10.1016/0025-5564(88)90064-8.
   Web of Science ®Google Scholar
• Mackey MC, Glass L. 1977. Oscillation and chaos in physiological control systems. Science. 197(4300):287–289. doi: 10.1126/science.267326.
   PubMed Web of Science ®Google Scholar
• Mayer H, Zaenker KS, An Der Heiden U. 1995. A basic mathematical model of the immune response. Chaos: An Interdisciplinary J Nonlinear Sci. 5(1):155–161. doi: 10.1063/1.166098.
   PubMed Web of Science ®Google Scholar
• Phaneendra K, Lalu M. 2019. Numerical solution of singularly perturbed delay differential equations using gaussion quadrature method. J Phys Conf Ser. 1344(1):012013. doi: 10.1088/1742-6596/1344/1/012013.
   Google Scholar
• Sekar E, Tamilselvan A. 2019. Singularly perturbed delay differential equations of convection–diffusion type with integral boundary condition. J Appl Math Comput. 59(1–2):701–722. doi: 10.1007/s12190-018-1198-4.
   Web of Science ®Google Scholar
• Selvi PA, Ramanujam N. 2017. An iterative numerical method for a weakly coupled system of singularly perturbed convection–diffusion equations with negative shifts. Int J Appl Comput Math. 3(S1):147–160. doi: 10.1007/s40819-017-0346-0.
   Google Scholar
• Subburayan V, Ramanujam N. 2014. An asymptotic numerical method for singularly perturbed weakly coupled system of convection–diffusion type differential difference equations. Novi Sad J Math. 44(2):53–68.
   Google Scholar
• Woldaregay MM, Liu L. 2022. Solving singularly perturbed delay differential equations via fitted mesh and exact difference method. Res Math. 9(1):2109301. doi: 10.1080/27684830.2022.2109301.
   Google Scholar