We investigate sufficient conditions for the existence and uniqueness of solutions to the boundary-value problems for integrodifferential equations with many delays. We propose and substantiate an iterative approximation scheme for the boundary-value problem with delay by a boundary-value problem for a system of ordinary differential equations.
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References
J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lect. Notes Biomath., 20, Springer, Berlin–New York (1977).
C. Tunc, “Properties of solutions to Volterra integro-differential equations with delay,” Appl. Math. Inf. Sci., 10, No. 5, 1775–1780 (2016).
H. Brunner, “Recent advances in the numerical analysis of Volterra functional differential equations with variable delays,” J. Comput. Appl. Math., 228, No. 2, 524–537 (2009).
N. P. Nastas’eva and I. M. Cherevko, “Approximate method for solving boundary-value problems for integrodifferential equations of neutral type,” Mat. Stud., 10, No. 2, 147–152 (1998).
I. Cherevko and A. Dorosh, “Existence and approximation of a solution of boundary-value problems for delay integro-differential equations,” J. Numer. Anal. Approx. Theory, 44, No. 2, 154–165 (2016).
A. Halanay, “Approximations of delays by ordinary differential equations,” in: R. Confi (editor), Recent Advances in Differential Equations, Academic Press, New York (1981), pp. 155–197.
O. V. Matvii and I. M. Cherevko, “On approximation of systems with delay and their stability,” Nelin. Kolyv., 7, No. 2, 208–216 (2004); English translation: Nonlin. Oscillat., 7, No. 2, 207–215 (2004).
O. A. Matvii and I. M. Cherevko, “Approximation of boundary-value problems with delay by systems of ordinary differential equations,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk, No. 3, 129–137 (2003).
L. J. Grim and K. Schmitt, “Boundary-value problems for delay-differential equations,” Bull. Amer. Math. Soc., 74, No. 5, 997–1000 (1968).
L. A. Piddubna and I. M. Cherevko, “Approximation of systems of differential-difference equations by systems of ordinary differential equations,” Nelin. Kolyv., 2, No. 1, 42–50 (1999).
O. V. Matvii and I. M. Cherevko, “Approximation of systems of differential-difference and difference equations with many delays,” Nauk. Visn. Cherniv. Univ.: Zb. Nauk. Prats Matematyka, Issue 150, 50–54 (2002).
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Translated from Neliniini Kolyvannya, Vol. 26, No. 1, pp. 33–41, January–March, 2023.
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Dorosh, A.B., Tuzyk, I.I. & Cherevko, I.M. Approximation Schemes for the Boundary-Value Problems for Integrodifferential Equations with Delay. J Math Sci 278, 963–973 (2024). https://doi.org/10.1007/s10958-024-06974-9
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DOI: https://doi.org/10.1007/s10958-024-06974-9