Numerical implementation of solving a boundary value problem including both delay and parameter

References

[1] Agarwal, R. P.—Chow, Y. M.: Finite difference methods for boundary value problems of differential equations with deviating arguments, Comput. Math. Appl. 12A(11) (1986), 1143–1153.10.1016/0898-1221(86)90018-0Search in Google Scholar

[2] Akhmetov, M. U.—Zafer, A.—Sejilova, R. D.: The control of boundary value problems for quasi lin-ear impulsive integro-differential equations, Nonlinear Anal. 48(2) (2002), 271–286.10.1016/S0362-546X(00)00186-3Search in Google Scholar

[3] Anderson, R. M.—May, R. M.: Infectious Diseases Of Humans: Dynamics and Control, Oxford University Press, USA, 1992.10.1093/oso/9780198545996.001.0001Search in Google Scholar

[4] Assanova, A. T.—Bakirova, E. A.—Kadirbayeva, Zh. M.—Uteshova, R. E.: A computational method for solving a problem with parameter for linear systems of integro-differential equations, Comput. Appl. Math. 39 (2020), Art. No. 248.10.1007/s40314-020-01298-1Search in Google Scholar

[5] Bakirova, E. A.—Assanova, A. T.—Kadirbayeva, Zh. M.: A problem with parameter for the integro-differential equations, Math. Model. Anal. 26(1) (2021), 34–54.10.3846/mma.2021.11977Search in Google Scholar

[6] Bakirova, E. A.—Iskakova, N. B.—Assanova, A. T.: Numerical method for the solution of linear boundary-value problems for integrodifferential equations based on spline approximations, Ukrainian Math. J. 71(9) (2020), 1341–1358.10.1007/s11253-020-01719-8Search in Google Scholar

[7] Bakirova, E. A.—Iskakova, N. B.—Kadirbayeva, Zh. M.: Numerical implementation for solving the boundary value problem for impulsive integro-differential equations with parameter, J. Math. Mech. Comput. S. 119(3) (2023), 19–29.10.26577/JMMCS2023v119i3a2Search in Google Scholar

[8] Bakke, V. L.—Jackiewicz, Z.: The numerical solution of boundary value problems for differential equations with state dependent deviating arguments, Appl. Math. 34 (1989), 1–17.10.21136/AM.1989.104330Search in Google Scholar

[9] Bellen, A.—Zennaro, M.: A collocation method for boundary value problems of differential equations with functional arguments, Computing 32 (1984), 307–318.10.1007/BF02243775Search in Google Scholar

[10] Blaha, K.—Lehnert, J.—Keane, A.—Dahms, T.—Hovel, P.—Scholl, E.—Hudson, J. L.: Clustering in delay-coupled smooth and relaxational chemical oscillators, Phys. Rev. E. 88(6) (2013), Art. ID 062915.10.1103/PhysRevE.88.062915Search in Google Scholar PubMed

[11] Cimen, E.: Numerical solution of a boundary value problem including both delay and boundary layer, Math. Model. Anal. 23(4) (2018), 568–581.10.3846/mma.2018.034Search in Google Scholar

[12] Derstein, M. W.—Gibbs, H. M.—Hopf, F. A.—Kaplan, D. L.: Bifurcation gap in a hybrid optically bistable system, Phys. Rev. A 26(6) (1982), 3720–3722.10.1103/PhysRevA.26.3720Search in Google Scholar

[13] Dzhumabaev, D.: Conditions the unique solvability of a linear boundary value problem for an ordinary differential equations, Comput. Math. Math. Phys. 29(1) (1989), 34–46.10.1016/0041-5553(89)90038-4Search in Google Scholar

[14] Dzhumabaev, D.: On one approach to solve the linear boundary value problems for Fredholm integro-differential equations, J. Comput. Appl. Math. 294 (2016), 342–357.10.1016/j.cam.2015.08.023Search in Google Scholar

[15] Dzhumabaev, D. S.—Bakirova, E. A.—Mynbayeva, S. T.: A method of solving a nonlinear boundary value problem with a parameter for a loaded differential equation, Math. Methods Appl. Sci. 43(4) (2020), 1788–1802.10.1002/mma.6003Search in Google Scholar

[16] DžUrina, J.—BaculíKová, B.: New oscillatory criteria for third-order differential equations with mixed argument, Math. Slovaca 74(5) (2024), 1233–1240.10.1515/ms-2024-0089Search in Google Scholar

[17] Erneux, T.: Applied Delay Differential Equations. Surveys and Tutorials in the Applied Mathematical Sciences, Springer, New York, 2009.10.1007/978-0-387-74372-1_8Search in Google Scholar

[18] Evans, D. J.—Raslan, K. R.: The Adomian decomposition method for solving delay differential equations, Int. J. Comput. Math. 82(1) (2005), 49–54.10.1080/00207160412331286815Search in Google Scholar

[19] Grace, S. R.—Graef, J. R.—Tunc, E.: On oscillatory behavior of third order half-Linear delay differential equations, Math. Slovaca 73(3) (2023), 729–736.10.1515/ms-2023-0053Search in Google Scholar

[20] Iskakova, N. B.—Bakirova, E. A.—Khanzharova, B. S.—Kadirbayeva, Zh. M.: An algorithm for solving boundary value problems for delay differential equations with loadings, Lobachevskii J. Math. 45(10) (2024), 5032–5042.10.1134/S1995080224606064Search in Google Scholar

[21] Iskakova, N.—Temesheva, S.—Uteshova, R.: On a problem for a delay differential equations, Math. Methods Appl. Sci. 46(9) (2023), 11283–11297.10.1002/mma.9181Search in Google Scholar

[22] Ishak, F.—Suleiman, M. B.—Omar, Z.: Two-point predictor-corrector block method for solving delay differential equations, Matematika 24(2) (2008), 131–140.Search in Google Scholar

[23] Jaaffar, N. T.—Abdulmajid, Z.—Senu, N.: Numerical approach for solving delay differential equations with boundary conditions, Mathematics 8(7) (2020), Art. No. 1073.10.3390/math8071073Search in Google Scholar

[24] De Jong, H.: Modeling And Simulation Of Genetic Regulatory Systems: A literature review, J. Comput. Biol. 9 (2002), 67–103.10.1089/10665270252833208Search in Google Scholar PubMed

[25] Kadirbayeva, Zh. M.—Bakirova, E. A.—Tleulessova, A. B.: Solving Fredholm Integro-Differential Equations Involving Integral Condition: A new numerical method, Math. Slovaca 74(2) (2024), 403–416.10.1515/ms-2024-0031Search in Google Scholar

[26] Kadirbayeva, Zh. M.—Kabdrakhova, S. S.: A numerical solution of problem for essentially loaded differential equations with an integro-multipoint condition, Open Math. 20(1) (2022), 1173–1183.10.1515/math-2022-0496Search in Google Scholar

[27] Keane, A.—Krauskopf, B.—Postlethwaite, C. M.: Climate models with delay differential equations, Chaos 27(11) (2017), Art. No. 114309.10.1063/1.5006923Search in Google Scholar PubMed

[28] Kolesov, Y. S.—Shvitra, D.: Role of time-delay in mathematical models of ecology, Lith. Math. J. 19 (1979), 81–91.10.1007/BF00972005Search in Google Scholar

[29] Kuang, Y.: Delay Differential Equations. With Applications in Population Dynamics, Academic Press, Boston, 2012.Search in Google Scholar

[30] Kyrychko, Y. N.—Blyuss, K. B.: Global properties of a delayed sir model with temporary immunity and nonlinear incidence rate, Nonlinear Anal. Real World Appl. 6 (2005), 495–507.10.1016/j.nonrwa.2004.10.001Search in Google Scholar

[31] Longtin, A.—Milton, J. G.: Complex oscillations in the human pupil light reflex with “mixed” and delayed feedback, Math. Biosci. 90(1–2) (1988), 183–199.10.1016/0025-5564(88)90064-8Search in Google Scholar

[32] Okeke, G. A.—Udo, A. V.—Alqahtani, R. T.—Kaplan, M.—Ahmed, W. E.: A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green’s functions, AIMS Math. 9(3) (2024), 6468–6498.10.3934/math.2024315Search in Google Scholar

[33] Rasdi, N.—Majid, Z. A.—Ismail, F.—Senu, N.—Phang, P. S.—Radzi, H. M.: Solving second order delay differential equations by direct two and three point one-step block method, Appl. Math. Sci. 7(54) (2013), 2647–2660.10.12988/ams.2013.13237Search in Google Scholar

[34] Ronto, M.—Samoilenko, A. M.: Numerical-Analytic Methods in the Theory of Boundary-Value Problems, World Scientific, River Edge, NJ, 2000.10.1142/9789812813602Search in Google Scholar

[35] Sakai, M.: Numerical solution of boundary value problems for second order functional differential equations by the use of cubic splines, Mem. Fac. Sci. Kyushu Univ. Ser. A Math. 29 (1975), 113–122.10.2206/kyushumfs.29.113Search in Google Scholar

[36] Scholl, E.—Hiller, G.—Hovel, P.—Dahlem, M. A.: Time-delayed feedback in neurosystems, Philos. Trans. Roy. Soc. A 367 (2009), 1079–1096.10.1098/rsta.2008.0258Search in Google Scholar PubMed

[37] Seong, H. Y.—Majid, Z. A.: Solving second order delay differential equations using direct two-point block method, Ain Shams Eng. J. 8(1) (2017), 59–66.10.1016/j.asej.2015.07.014Search in Google Scholar

[38] Stein, R. B.: Some models of neuronal variability, Biophys. J. 7(1) (1967), 37–68.10.1016/S0006-3495(67)86574-3Search in Google Scholar PubMed PubMed Central

[39] Temesheva, S. M.—Dzhumabaev, D. S.—Kabdrakhova, S. S.: On one algorithm to find a solution to a linear two-point boundary value problem, Lobachevskii J. Math. 42(3) (2021), 606–612.10.1134/S1995080221030173Search in Google Scholar

[40] Uteshova, R. E.—Kadirbayeva, Zh. M.—Marat, G.—Minglibayeva, B. B.: A novel numerical implementation for solving problem for loaded depcag, Int. J. Math. Phys. 13(2) (2022), 50–57.10.26577/ijmph.2022.v13.i2.07Search in Google Scholar