Numerical solution of nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets

Abstract

Abstract In this paper, an efficient numerical method is presented for solving nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets. By the properties of Haar wavelets and stochastic integration operational matrixes, the approximate solution of nonlinear stochastic Itô–Volterra integral equations can be found. At the same time, the error analysis is established. Finally, two numerical examples are offered to testify the validity and precision of the presented method.

Keywords

• Haar wavelets
• Stochastic integration operational matrixes
• Stochastic Itô–Volterra integral equations