Refined Unbiased Stochastic Approach for Fredholm Integral Equations

Abstract Integral equations are highly relevant across various fields such as applied mathematics, physics, engineering, geophysics, electromagnetism, the kinetic theory of gases, quantum mechanics, mathematical economics, and queuing theory. This underscores the importance of creating and examining efficient and dependable methods to solve integral equations. In the context of multidimensional issues, traditional biased stochastic algorithms, which rely on a finite set of integration points, are particularly challenged by the complexities of higher dimensionality. Therefore, it is critical to develop sophisticated unbiased algorithms to address these challenges, as discussed in this paper. We introduce and evaluate a novel unbiased stochastic approach for solving multidimensional Fredholm integral equations of the second kind.