‎A spectral collocation method‎ for solving stochastic fractional integro-differential equation - Mahsa Zaboli; Haleh Tajadodi (Mathematics and Computational Sciences, 2025)
In this paper‎, ‎a numerical scheme based on shifted Vieta-Lucas polynomials is utilised to solve mentioned equation‎. ‎The main characteristic of the presented method is to approximate Brownian motion with help of the Gauss-Legendre quadrature‎, ‎which makes calculations easier‎. ‎Another characteristic of this method are employed suitable collocation points to convert the stochastic equation under the study into a system of algebraic equations by using the operational matrices‎. ‎So that‎, ‎Newton's method is applied to solve them‎. The convergence analysis and error bound of the suggested method are well established‎. ‎Additionally‎, ‎the proofs related to the existence and uniqueness of the solutions for the equations under investigation have been provided‎. ‎In order to illustrate the effectiveness‎, ‎compatibility and plausibility of the proposed technique‎, ‎four numerical examples are presented.