Computational Methods for Stochastic Differential Equations and Stochastic Partial Differential Equations Involving Standard Brownian and Fractional Brownian Motion

As more applied science researchers are attempting to use Stochastic Differential Equations (SDEs) as well as Stochastic Partial Differential Equations (SPDEs) in their modeling, especially when involving Fractional Brownian Motion (fBM), one common issue appears: an exact solution cannot always be found. For cases involving SPDEs, exact solutions commonly do not exist and approximation schemes for their solution are typically still in development. Therefore, in this paper, we test various Numerical methods in solving SDEs and SPDEs with standard BM that have non-linear coeffi cients. In addition we extend our results to problems with fBM.