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Mixed two-grid finite difference methods for solving one-dimensional and two-dimensional Fitzhugh-Nagumo equations
- Source :
- Mathematical Methods in the Applied Sciences. 40:1170-1200
- Publication Year :
- 2016
- Publisher :
- Wiley, 2016.
-
Abstract
- The aim of this paper is to propose mixed two-grid finite difference methods to obtain the numerical solution of the one-dimensional and two-dimensional Fitzhugh–Nagumo equations. The finite difference equations at all interior grid points form a large-sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a family of finite difference methods for discretizing the spatial and time derivatives. The obtained system has been solved by two-grid method, where the two-grid method is used for solving the large-sparse linear systems. Also, in the proposed method, the spectral radius with local Fourier analysis is calculated for different values of h and Δt. The numerical examples show the efficiency of this algorithm for solving the one-dimensional and two-dimensional Fitzhugh–Nagumo equations. Copyright © 2016 John Wiley & Sons, Ltd.
- Subjects :
- Partial differential equation
General Mathematics
Mathematical analysis
General Engineering
Numerical methods for ordinary differential equations
Finite difference method
Finite difference
Finite difference coefficient
010103 numerical & computational mathematics
Mixed finite element method
01 natural sciences
010101 applied mathematics
Multigrid method
0101 mathematics
Mathematics
Numerical partial differential equations
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........bcfba404ff2720a3c0f8814cd16f5149