Using Two-Dimensional Bernstein Polynomials to Simulate Two-Dimensional Linear Stochastic Fredholm Integral Equations with Multiple Noise Sources

Résumé

‎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.