Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations

Abstract

We present a new technique for solving numerically stochastic Volterra integral equation based on modified block pulse functions. It declares that the rate of convergence of the presented method is faster than the method based on block pulse functions. Efficiency of this method and good degree of accuracy are confirmed by a numerical example.

A novel numerical approach based on shifted second‐kind Chebyshev polynomials for solving stochastic Itô–Volterra integral equation of Abel type with weakly singular kernel

“…To solve deterministic IEs or SIEs, a variety of numerical approaches are developed. Bernstien polynomials [8,9], orthonormal Bernoulli polynomials (OBPs) [10], block pulse functions [11], Chebyshev wavelets [12], Legendre polynomials [13], shifted Jacobi operational matrix [14], shifted Legendre polynomials [15], meshless local discrete Galerkin scheme [16], wavelets Galerkin method [17], generalized hat basis functions [18], Legendre wavelets Galerkin method [19], Chebyshev cardinal wavelets [20,21], and so on are utilized to determine the solution for different types of IEs.…”

Study of hybrid orthonormal functions method for solving second kind fuzzy Fredholm integral equations

“…The improved block-pulse function is introduced by Farshid Mirzaee [41]. These modified block-pulse functions are applied to numerical solution of stochastic Volterra integral equations [42]. The Bernstein polynomials (BPs) and improved block-pulse functions (IBPFs) are introduced in [43].…”

Numerical solution of linear stochastic Volterra integral equations via new basis functions

“…Asgari et al suggested stochastic operational matrix based on Bernstein polynomials for obtaining numerical solution of nonlinear stochastic integral equation [7]. K.Maleknejad et al used modified block pulse functions for solving stochastic Volterra integral equations [8].S. Bhattacharya et al have obtained numerical solutions of Volterra integral equations by applying Bernstien polynomials [9].…”