Collocation methods for nonlinear stochastic Volterra integral equations

Abstract

Influenced by Xiao et al. (J Integral Equations Appl 30(1):197–218, 2018), collocation methods are developed to study strong convergence orders of numerical solutions for nonlinear stochastic Volterra integral equations under the Lipschitz condition in this paper. Some properties of exact solutions are discussed. These properties include the mean-square boundedness, the Holder condition, and conditional expectations. In addition, this paper considers the solvability, the mean-square boundedness, and strong convergence orders of numerical solutions. At last, we validate our conclusions by numerical experiments.