Numerical solution of nonlinear stochastic Itô-Volterra integral equations driven by fractional Brownian motion using triangular functions

The paper proposes an efficient global approximation method via triangular functions (TFs) to solve stochastic Itô-Volterra integral equations (SIVIEs) driven by fractional Brownian motion (fBm) with Hurst parameter H∈((1/2),1). By the relevant knowledge of TFs and fBm, new stochastic integral operator matrices with regard to fBm are derived, thus the nonlinear SIVIEs can be converted into nonlinear algebraic equations. Furthermore, the error analysis of the method was carried out to demonstrate its higher error order. Finally, the feasibility and effectiveness of the approach are verified by two numerical examples and an application in mathematical ecology.