On numerical solution of the second-order linear Fredholm–Stieltjes integral equation
Source abstract
Abstract
In this framework, the necessary and sufficient conditions for the existence and uniqueness of the second-order linear Fredholm–Stieltjes-integral equations, u(x)=λ∫abK(x,y)u(y)dg(y)+f(x),x∈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 limited cases.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Numerical methods for differential equations · Differential Equations and Numerical Methods
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Affiliations
Department of Mathematics and Natural Sciences, School of Arts and Sciences, University of Central Asia 1 , 310 Lenin Street, 722918 Naryn, Kyrgyzstan
Department of Mathematics, Kyrgyz-Turkish Manas University, Chyngyz Aitmatov Campus 2 , 720038 Djal, Bishkek, Kyrgyzstan
References (17)
Show source-provided references
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