On solving a singular Volterra integral equation


Ramazanov M.I. Gulmanov N.K. Omarov M.T.
2025University of Nis

Filomat
2025#39Issue 113647 - 3656 pp.

In the paper, a general solution of the singular Volterra integral equation of the second kind is found. The feature of the considered integral equation lies in the fact that the integral of its kernel does not tend to zero as the upper limit approaches the lower one, thus making the Picard method inapplicable. It is shown that the corresponding homogeneous integral equation has a non-zero solution, which is found in an explicit form. Such integral equations arise, for example, in boundary value problems of heat conduction in degenerate regions, where the boundaries change with time [10]-[2]. Additionally, these equations appear in mathematical modeling of thermophysical processes in the electric arc of high-current switching devices [8]-[7].

characteristic numbers , eigenfunction of the Volterra equation , general solution , homogeneous equation , resolvent , singular second-kind Volterra integral equation

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Karaganda Buketov University, Karaganda, 100028, Kazakhstan

Karaganda Buketov University

10 лет помогаем публиковать статьи Международный издатель

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