ABSTRACT In this paper, we propose an ‐splitting iteration method for solving the all‐at‐once system of weakly nonlinear equations. The system arises from the discrete semi‐linear diffusion equation with a Caputo fractional derivative. We employ L1 formula and the standard central difference scheme to discretize time and space, respectively. We then introduce the ‐splitting iteration method to tackle the all‐at‐once system of weakly nonlinear equations. Furthermore, we establish local and global convergence theories for the proposed iteration method under certain assumptions. Numerical results demonstrate that this method is effective for solving the all‐at‐once nonlinear system.
Li et al. (Wed,) studied this question.