A Fifth (Six) Order Accurate, Three-Point Compact Finite Difference Scheme for the Numerical Solution of Sixth Order Boundary Value Problems on Geometric Meshes

2014 ◽  
Vol 64 (3) ◽  
pp. 898-913 ◽  
Author(s):  
Navnit Jha ◽  
Lesław K. Bieniasz
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Finite Difference Scheme ◽  
Boundary Value ◽  
Sixth Order ◽  
Compact Finite Difference Scheme ◽  
Compact Finite Difference

A Fourth-Order Compact Finite Difference Scheme to the Numerical Solution of FitzHugh-Nagumo Equation

2017 ◽  
Vol 873 ◽  
pp. 337-341
Author(s):  
Dan Ping Gui
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Fourth Order ◽  
Difference Method ◽  
Finite Difference Scheme ◽  
Reaction Diffusion Equation ◽  
Compact Finite Difference Scheme ◽  
Compact Finite Difference ◽  
Nagumo Equation

The FitzHugh-Nagumo equation is an important nonlinear reaction-diffusion equation used in physics and chemicals. To obtain the numerical solution of partial differential equations, the compact finite difference method is widely applied. In this paper, I propose a new numerical solution to FitzHugh-Nagumo equation by using a fourth-order compact finite difference scheme in space, and a semi-implicit Crank-Nicholson method in time. I further calculate the results in terms of accuracy by leveraging the proposed method and exact solution. In particular, I compare the new method whose convergence order is close to four with the second order central difference method. The simulated results show the new solution is more accurate and effective. The proposed method is expected to be a good solution to some problems in the real world.

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