Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations

In various fields of science and engineering, such as financial mathematics, mathematical physics models, and radiation transfer, stochastic integral equations are important and practical tools for modeling and describing problems. Due to the existence of random factors, we face a fundamental problem in solving stochastic integral equations, and that is the lack of analytical solutions or the great complexity of these solutions. Therefore, finding an efficient numerical solution is essential. In this paper, we intend to propose and study a new method based on the Floater-Hormann interpolation and the spectral collocation method for linear and nonlinear stochastic Itô-Volterra integral equations (SVIEs). The Floater-Hormann interpolation offers an approximation regardless of the distribution of the points. Therefore, this method can be mentioned as a meshless method. The presented method reduces SVIEs under consideration into a system of algebraic equations that can be solved by the appropriate method. We presented an error bound to be sure of the convergence and reliability of the method. Finally, the efficiency and the applicability of the present scheme are investigated through some numerical experiments.