A linearly implicit scheme and fast multigrid solver for 3D Fitzhugh-Nagumo equation. (1st July 2022) - Wu, Pinxia; Pan, Kejia; Ling, Weiwei; Wu, Qihong
Abstract: In this work, a second-order finite difference (FD) scheme for three-dimensional (3D) nonlinear Fitzhugh-Nagumo (FN) equation with the nonlinear term treated with semi-implicitly technique is proposed. The existence and uniqueness of the difference scheme is proved, and the stability and convergence of numerical solution in L ∞ -norm are also shown. Then, we employ an efficient extrapolation cascadic multigrid (EXCMG) method to solve the large linear system arising from the proposed second-order FD discretization for the 3D FN equation. Numerical results are presented to verify our theoretical findings of the difference scheme and the efficiency of the EXCMG method. The EXCMG method can also be extended to solve other kinds of time-dependent nonlinear partial differential equations.