Advances in Differential Equations and Control Processes
Volume 31, Issue 2, Pages 285 - 297
(June 2024) http://dx.doi.org/10.17654/0974324324015 |
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PERIODIC SOLUTIONS OF A SECOND-ORDER NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION
A. T. Alymbaev, A. Bapa Kyzy and F. K. Sharshembieva
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Abstract: The article considers the problem of constructing a -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 -periodic solution to the integral equation is found using the projection-iteration method. A -periodic solution is sought as the limit of successive -periodic functions representable as a Fourier series. An estimate of the error of the difference between the exact and approximate solutions is obtained. |
Keywords and phrases: 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
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