A new hybrid approach for nonlinear stochastic differential equations driven by multifractional Gaussian noise

Abstract

The purpose of this paper is to present a new and efficient computational method based on the hybrid of block‐pulse functions and shifted Legendre polynomials together with their exact operational vector of integration and stochastic operational matrix of integration with respect to the multifractional Brownian motion to approximate solutions of a class of nonlinear stochastic differential equations driven by multifractional Gaussian noise. The presented method transforms problems under consideration into systems of nonlinear equations which can be simply solved by the Newton method. Moreover, the convergence analysis of the presented method is investigated. Finally, the efficiency of the new method is illustrated by solving the stochastic logistic equation and three test problems.