The extended Fisher--Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biology systems. In this talk, we discuss a full-rank splitting scheme and a rank-adaptive splitting approach for this equation. We first use a finite difference method to approximate the space derivatives and  then we split the resulting semi-discrete system into two stiff linear parts and a nonstiff nonlinear part. This leads to our full-rank splitting scheme.  Based on the frame of the full-rank splitting scheme,  we propose a rank-adaptive splitting approach for obtaining a low-rank solution.