A linearly implicit scheme and fast multigrid solver for 3D Fitzhugh-Nagumo equation
A linearly implicit scheme and fast multigrid solver for 3D Fitzhugh-Nagumo equation
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3D Fitzhugh-Nagumo 方程的线性隐式方案和快速多重网格求解器
DOI：
10.1016/j.camwa.2022.05.003
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发表时间：
2022-07
影响因子：
2.9
通讯作者：
Qihong Wu
中科院分区：
文献类型：
--
作者：
Pin-Xia Wu;Kejia Pan;Weiwei Ling;Qihong Wu
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.
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