Numerical solution of stochastic Itô-Volterra integral equations driven by fractional Brownian motion using quintic B-spline collocation method

In this article, stochastic It & ocirc;-Volterra integral equations driven by fractional Brownian motion have been solved by the quintic B-spline collocation method. This approach is based on a quintic B-spline interpolation, Gauss-Legendre quadrature formula, and It & ocirc; approximation. The main characteristic of the proposed method is that it reduces stochastic It & ocirc;-Volterra integral equations driven by fractional Brownian motion into a system of algebraic equations. Then, Newton's method is applied to obtain the desired approximate solution. Furthermore, the convergence analysis of the presented method is discussed in detail. Some numerical instances are discussed to show the applicability and accuracy of the proposed method. Also, numerical results obtained by the quintic B-spline collocation method are compared with the existing shifted Chebyshev wavelets method, which shows the efficiency of the discussed method.