The error estimation in terms of the first derivative in a numerical method for the solution of a delay integral equation from biomathematics

Alexandru Bica

doi:10.33993/jnaat341-788

Authors

Alexandru Bica University of Oradea, Romania

DOI:

https://doi.org/10.33993/jnaat341-788

Keywords:

delay integral equation, successive approximations, trapezoidal quadrature rule

Abstract views: 223

Abstract

The positive, bounded and smooth solution of a delay integral equation, which arise in epidemics spread, can be found in an approximative manner using numerical methods achieved by the sequence of successive approximations and quadrature rules classified after the properties of the function \(f\), such as Lipschitzian or in the \(C^{1}\) smoothness case.

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References

Cerone, P., Dragomir, S.S., Trapeziodal and Midpoint-Type Rules from Inequalities Point of View (ch. 3 and 4 in Handbook of "Analytic Computational Methods in Applied Mathematics", ed. G. Anastassiou), Chapman&Hall/CRC, New York, 2000. DOI: https://doi.org/10.1201/9781420036053.ch4

Cerone, P. Dragomir, S.S., Three point quadrature rules involving, at most, at first derivative, RGMIA (preprint), 2, no. 4, pp. 511-583, 1999.

Guo, D. Lakshmikantham, V., Positive solutions of nonlinear integral equations arising in infectious diseases, J. Math. Anal. Appl., 134, pp. 1-8, 1988, https://doi.org/10.1016/0022-247x(88)90002-9 DOI: https://doi.org/10.1016/0022-247X(88)90002-9

Iancu, C., A numerical method for approximating the solution of an integral equation from biomathematics, Studia Univ. "Babeş-Bolyai", Mathematica, XLIII, no. 4, pp. 37-45, 1998.

Precup, R., Positive solutions of the initial value problem for an integral equation modelling infectious disease, Seminar on Fixed Point Theory, Preprint no. 3, ed. I.A. Rus, pp. 25-30, 1991.

Precup, R., Periodic solutions for an integral equation from biomathematics via Leray-Schauder principle, Studia Univ. "Babeş-Bolyai", Mathematica, XXXIX, no. 1, pp. 47-58, 1994.

Precup, R., Monotone technique to the initial values problem for a delay integral equation from biomathematics, Studia Univ. "Babeş-Bolyai", Mathematica, XL, no. 2, pp. 63-73, 1995.

Rus, I. A., A delay integral equation from biomathematics, Seminar of Differential Equations, Preprint, no. 3, pp.87-90, 1989.

Rus, I. A., Differential equations, integral equations and dynamical systems, Transilvania Press, Cluj Napoca, 1996 (in Romanian).