A scheme for finding approximate solutions to boundary value problems for neutral-type integro-differential equations with variable argument deviation is studied, based on the suggested iterative scheme using cubic splines with the defect two. For a practical modeling of such boundary value problems, an application with a user-friendly interface for setting input parameters and visualizing the results has been developed.

[1] Cushing J.M. Integrodifferential equations and delay models in population dynamics. Lecture Notes in Biomathematics, Vol. 20. Springer Verlag, Berlin-Heidelberg-New York, 1977.

[2] Yang Kuang. Delay differential equations: with applications in population dynamics. Academic Press, New York, 1993. 398 p.
[3] Forrest-Owen O. Mathematical Modelling and it's Applications in Biology, Ecology and Population Study. Master's Thesis, Chester, 2016. 124 p.
[4] Luchka A., Feruk, V. Projection-iterative method for systems of differential equations with delay and constraints. Nonlinear oscillations, 2003, 6 (2), 206-232. (in Ukrainian)
[5] Bellour A., Bousselsal M. Numerical Solution of Delay Integro-Differential Equations by Using Taylor Collocation Method. Mathematical Methods in Applied Science, 2014, 37, 1491-1506. doi:10.1002/mma.2910
[6] Nikolova T.S., Bainov D.D. Application of spline-functions for the construction of an approximate solution of boundary value problems for a class of functional-differential equations. Yokohama Math. J., 1981, 29 (1), 108-122.
[7] Cherevko I.,Dorosh A. Existence and Approximation of a Solution of Boundary Value Problems for Delay Integro-Differential Equations. J. Numer. Anal. Approx. Theory, 2015, 44 (2), 154-165. doi:10.33993/jnaat442-1054
[8] Halanay A. Approximations of delays by ordinary differential equations. Recent advances in differential equations. Academic Press, New York, 1981. Pp. 155-197.
[9] Cherevko I.Ì., Ìàtviy Î.V. On the approximation of systems with a delay and their stability. Nonlinear oscillations. 2004, 7 (2), 208-216.
[10] Dorosh A.B., Tuzyk I.I., Cherevko I.M. Approximation schemes for boundary value problems for integrodifferential equations with delay. Nonlinear oscillations. 2023, 26 (1), 33-41. (in Ukrainian)
[11] Dorosh A., Cherevko I. Boundary Value Problem Solution Existence For Linear Integro-Dierential Equations With Many Delays. Carpathian Mathematical Publications. 2018, 10 (1), 65-70. doi:10.15330/cmp.10.1.65-70
[12] Grim L.J., Schmitt K. Boundary value problems for delay differential equations. Bull. Amer. Math. Soc. 1968, 74 (5), 997-1000.
[13] Nastasieva N.P., Cherevko I.M. Approximate method for solving boundary value problems for neutral type integro-differential equations. Math Studios. 1998, 10 (2), 147-152. (in Ukrainian)