Spectral Galerkin Method Based on Chelyshkov Polynomials for Solving Stochastic Integral Equations

Abstract

Stochastic integral equations (SIEs) have gained significant attention recently due to their applications in various fields of science and engineering include turbulent flows, population dynamics, heat transfer problems, and the Black-Scholes option pricing model in mathematical finance. We use these equations to model real-world phenomena where uncertainty or randomness plays a critical role. This study presents an advanced numerical method approach to solving linear and non-linear SIEs through a spectral Galerkin method based on Chelyshkov polynomials. By employing this method, the intricate task of solving such equations is simplified into a set of algebraic equations that are efficiently solvable via any numerical method, such as Gauss elimination and Newton’s method. Furthermore, convergence analysis is also established. Lastly, Numerical results demonstrate the superiority of the suggested approach in terms of accuracy and computational efficiency.