PERIODIC SOLUTIONS OF A SECOND-ORDER NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION

A. T. Alymbaev; A. Bapa Kyzy; F. K. Sharshembieva

A. T. Alymbaev Arabaev Kyrgyz State University, Bishkek, Kyrgyzstan
A. Bapa Kyzy K. Tynystanov Issyk-Kul State University, Bishkek,Kyrgyzstan
F. K. Sharshembieva Zh.Balasagyn Kyrgyz National University, Bishkek, Kyrgyzstan

Article ID: 2438

Keywords: periodic solutions; quasilinear second-order integro-differential equations; Green’s function, integral equations on the number axis; exact and approximate solutions; method of successive approximations

Abstract

The article considers the problem of constructing a 2π-periodic solution of a quasilinear second-order integro-differential equation. Using the Green's function of bounded solutions on the number line, the integro-differential equation is reduced to an integral equation.A 2π-periodic solution to the integral equation is found using the projection-iteration method.A 2π- periodic solution is sought as the limit of successive 2π-periodic functions representable as a Fourier series. An estimate of the error of the difference between the exact and approximate solutions is obtained.

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