Implicit Euler approximation of stochastic evolution equations with fractional Brownian motion

•Numerical solution of stochastic fractional differential equations is proposed.•The spatial approximation method is based on Galerkin and the temporal approximation is based on implicit Euler scheme.•The order on convergence of implicit method for SFDEs is 1.

This work was intended as an attempt to motivate the approximation of quasi linear evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H>12. The spatial approximation method is based on Galerkin and the temporal approximation is based on implicit Euler scheme. An error bound and the convergence of the numerical method are given. The numerical results show usefulness and accuracy of the method.