New Technique Based on Vieta–Lucas Polynomials for Solving Nonlinear Stochastic Itô‐Volterra Integral Equation

ABSTRACT In the present study, we introduce an iterative technique grounded in shifted Vieta–Lucas polynomials for the numerical solution of nonlinear stochastic Volterra integral equations. Notably, our iterative approach is fast and provides solutions without solving algebraic equations. This method addresses nonlinear problems with high accuracy, making it very useful. We present an error estimation for the suggested approach, theoretically confirming its accuracy. Several numerical examples illustrate the practicality and efficacy of our technique. Furthermore, we compare the numerical outcomes of our method with those reported in existing literature and, whenever available, with exact solutions. This comparative analysis affirms the practicality and high precision of the suggested approach.