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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
