Intelligent Monte Carlo Approach for Solving Multidimensional Fredholm Integral Equations

Integral equations are widely used in a variety of disciplines. Consequently, developing and investigating effective and reliable methods for solving integral equations is of paramount importance. For problems involving multiple dimensions, current biased stochastic methods, which rely on a limited set of integrals and are dependent on quadrature points, are impeded by the complexity arising from high dimensionality. Therefore, there is a need for advanced, unbiased algorithms to address these multidimensional issues, which is the focus of our paper. We present a novel, unbiased stochastic approach for tackling multi-dimensional Fredholm integral equations of the second kind. This new method is thoroughly examined and contrasted with previous unbiased stochastic techniques, covering both single and multiple dimensions. The goal of this study is to deepen the understanding of unbiased stochastic methods and to enhance their efficacy and dependability in solving complex, multidimensional integral equations.