Using two-dimensional Bernstein polynomials to simulate two-dimensional linear stochastic fredholm integral equations with multiple noise source

Murtadha Ali Shabeeb‎; Mohsen  Fallahpour; Reza  Ezzati; Mohammad Navaz  Rasoulizadeh

doi:10.5269/bspm.77951

Murtadha Ali Shabeeb‎ Misan University‎,
Mohsen Fallahpour Department of Mathematics‎, ‎Karaj Branch‎, ‎Islamic Azad University‎, ‎Karaj 31499-68111‎, ‎Iran
Reza Ezzati Department of Mathematics‎, ‎Karaj Branch‎, ‎Islamic Azad University‎, ‎Karaj 31499-68111‎, ‎Iran
Mohammad Navaz Rasoulizadeh Department of Mathematics‎, ‎Velayat University‎, ‎Iranshahr 99176-38733‎, ‎Iran

Abstract

‎This paper presents a numerical method utilizing two-dimensional Bernstein polynomials (2DBPs) to efficiently solve systems of two-dimensional linear multi-noise stochastic Fredholm integral equations (2D-LMN-SFIEs)‎. ‎The methodology is supported by a series of theorems that establish the convergence of the approach and highlight its distinct benefits‎. ‎To validate the method’s performance‎, ‎it is tested on two examples‎, ‎which emphasize its precision and practical relevance‎. ‎These examples illustrate the method's strength in managing complex stochastic integral equations‎, ‎confirming its significance for both theoretical and practical applications in mathematics‎.

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