Numerical solution for stochastic extended Fisher-Kolmogorov equation

In this paper, we derived a new compact finite difference scheme in the spatial direction and used the semi-implicit Euler-Maruyama approach in the temporal direction to study a stochastic extended Fisher-Kolmogorov equation with multiplicative noise numerically. Moreover, the analysis of consistency for the stochastic difference scheme was discussed and the stability analysis was proven in the mean square sense and by Fourier analysis. This approach is numerically analyzed to show the effect of random fluctuations occurring in nature and missing from the deterministic version of the equation and this illustrated in a numerical experiment.