PERIODIC SOLUTIONS OF A SECOND-ORDER NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION
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 approximationsDOI:
https://doi.org/10.17654/0974324324015Abstract
The article considers the problem of constructing a $2 \pi$-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 $2 \pi$-periodic solution to the integral equation is found using the projection-iteration method. A $2 \pi$-periodic solution is sought as the limit of successive $2 \pi$-periodic functions representable as a Fourier series. An estimate of the error of the difference between the exact and approximate solutions is obtained.
Received: February 18, 2024
Revised: April 29, 2024
Accepted: May 9, 2024
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