Approximation approach for backward stochastic Volterra integral equations

In this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. We used Newton's technique to solve a particular BSVIE by employing block pulse functions (BPFs) and the related stochastic operational matrix of integration. Additionally, we developed considerations for Lipschitz and linear growth, along with linearity conditions, to illustrate error and convergence analysis. We compared the solutions we obtain the values of exact and approximate solutions at selected points with a defined absolute error. The computations were performed using MATLAB R2018a.