Study on Numerical Approach Solution of the System of Two-dimensional Fredholm Integral Equations by using Bernstein Polynomial

Kwon Un Gyong; Ri Kwang; Kim Yun Mi

doi:10.22161/ijcmp.9.4.4

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Study on Numerical Approach Solution of the System of Two-dimensional Fredholm Integral Equations by using Bernstein Polynomial

Kwon Un Gyong , Ri Kwang , Kim Yun Mi

International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-9,Issue-4, October - December 2025, Pages 28-44 , 10.22161/ijcmp.9.4.4

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Article Info: Received: 17 Sep 2025; Received in revised form: 15 Oct 2025; Accepted: 21 Oct 2025; Available online: 27 Oct 2025

Abstract:

Integral equations are extensively used in many physical models appearing in the field of plasma physics, atmosphere–ocean dynamics, ﬂuid mechanics, mathematical physics and many other disciplines of physics and engineering. In this paper, we establish new numerical technique for the solution of the system of two-dimensional Fredholm integral equations (2DFIEs) of both ﬁrst and second kinds on any finite interval. Our method which is based on Bernstein polynomial reduces the system of 2DFIEs to an algebraic linear system, and they can be solved using any standard rule. We also present convergence analysis and stability analysis of the proposed technique.

Keywords:

Bernstein polynomial, convergence, Fredholm Integral Equations, algebraic linear system, finite interval

References:

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Study on Numerical Approach Solution of the System of Two-dimensional Fredholm Integral Equations by using Bernstein Polynomial

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