Avıt ASANOV

Article | 2021 | AIP Advances11 ( 7 )

In this framework, the necessary and sufficient conditions for the existence and uniqueness of the second-order linear Fredholm-Stieltjes-integral equations, u(x) = lambda integral(b)(a) K(x, y) u(y) dg(y) + f(x), x is an element of[a, b], are thoroughly derived. Moreover, instead of approximating the integral equation by different numbers of partition n, the optimal number n for the given error tolerance is established. The system of equations is implemented in MAPLE for the Runge method. An efficient scheme is proposed for second-order integral equations. The solution has been compared with an exact and closed-form solution for li . . .mited cases. (c) 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) More less