Compact Finite Differences Method for FitzHugh-Nagumo Equation

Akkoyunlu, Canan

doi:10.32323/ujma.561873

Cited by 3 publications

(2 citation statements)

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“…Table 5 compares the L ∞ error norm using the proposed scheme with some available data from Akkoyunlu [9] for different values of N at time t = 0.2. With the proposed scheme, we have almost the same or even better accuracy in the numerical approximation after just four applications, while the scheme presented in Akkoyunlu [9] has reached similar accuracy after 20 time steps. As a result, the proposed scheme produced similar errors in fewer iterations, saving computational effort.…”

Section: Examplementioning

confidence: 99%

“…A nonlinear reaction-diffusion equation, the FitzHugh-Nagumo equation originated in science and technology, particularly in neurophysiology and population growth models, flame propagation, logistic population growth, nuclear reactor theory and catalytic chemical reactions. Some researchers have looked at finite difference and compact difference methods, as in [9][10][11], to obtain numerical solutions of FitzHugh-Nagumo equations.…”

Section: Introductionmentioning

confidence: 99%

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A Five-Step Block Method Coupled with Symmetric Compact Finite Difference Scheme for Solving Time-Dependent Partial Differential Equations

Kaur,

Singh,

Ritelli

2024

Symmetry

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In this article, we present a five-step block method coupled with an existing fourth-order symmetric compact finite difference scheme for solving time-dependent initial-boundary value partial differential equations (PDEs) numerically. Firstly, a five-step block method has been designed to solve a first-order system of ordinary differential equations that arise in the semi-discretisation of a given initial boundary value PDE. The five-step block method is derived by utilising the theory of interpolation and collocation approaches, resulting in a method with eighth-order accuracy. Further, characteristics of the method have been analysed, and it is found that the block method possesses A-stability properties. The block method is coupled with an existing fourth-order symmetric compact finite difference scheme to solve a given PDE, resulting in an efficient combined numerical scheme. The discretisation of spatial derivatives appearing in the given equation using symmetric compact finite difference scheme results in a tridiagonal system of equations that can be solved by using any computer algebra system to get the approximate values of the spatial derivatives at different grid points. Two well-known test problems, namely the nonlinear Burgers equation and the FitzHugh-Nagumo equation, have been considered to analyse the proposed scheme. Numerical experiments reveal the good performance of the scheme considered in the article.

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Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%