Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes

Namjoo, Mehran; Zibaei, Sadegh

doi:10.1007/s40314-016-0406-9

Cited by 20 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is no apt general technique to find the denominator function

\phi \left(\Delta t\right)

and to select which nonlinear terms are to be placed instead. Some special technique can be found in [50–53, 55–57]. Here we use an explicit exact finite difference scheme to find the denominator function.…”

Section: Nsfd Schemementioning

confidence: 99%

Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization

Verma

Rawani

2022

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we analyze and propose to compute the numerical solutions of a generalized Rosenau-KDV-RLW (Rosenau-Korteweg De Vries-Regularized Long Wave) equation based on the Haar wavelet (HW) collocation approach coupled with nonstandard finite difference (NSFD) scheme and quasilinearization. In the process of the numerical solution, the NSFD scheme is applied to discretize the first-order time derivative, Haar wavelets are applied on spatial derivatives and the non-linear term is taken care by quasilinearization technique. To discuss the efficiency of the method we compute L ∞ error and L 2 error. We also use discrete mass and energy conservation to check the accuracy of the proposed methodology. The computed results have been compared with the existing methods, for example, three-level average implicit finite difference technique, B-spline collocation, three-level linear conservative implicit finite difference scheme and conservative fourth-order stable finite difference scheme.

show abstract

“…There is no apt general technique to find the denominator function

\phi \left(\Delta t\right)

Section: Nsfd Schemementioning

confidence: 99%

Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization

Verma

Rawani

2022

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…In [12], an exact finite difference scheme is defined as a finite difference model for which the solution to the difference equation has the same general solution as the associated differential equation. Recently, there is an increasing interest to find exact finite difference models for particular PDEs, because these finite difference models do not exhibit numerical instabilities (see [22], [15] and [17]). However, not every PDE has exact finite difference model.…”

Section: Exact Finite Difference Schemes For B(2 2) Equationmentioning

confidence: 99%

Exact and nonstandard finite difference schemes for the Burgers equationB(2,2)

Köroğlu¹,

Aydın²

2021

Turk J Math

View full text Add to dashboard Cite

In this paper, we consider the Burgers equation B(2, 2). Exact and nonstandard finite difference schemes (NSFD) for the Burgers equation B(2, 2) are designed. First, two exact finite difference schemes for the Burgers equation B(2, 2) are proposed using traveling wave solution. Then, two NSFD schemes are represented for this equation. These two NSFD schemes are compared with a standard finite difference(SFD) scheme. Numerical results show that the NSFD schemes are accurate and efficient in the numerical simulation of the kink-wave solution of the B(2, 2) equation. We see that although the SFD scheme yields numerical instability for large step sizes, NSFD schemes provide reliable results for long time integration. Local truncation errors show that the NSFD schemes are consistent with the B(2, 2) equation.

show abstract

“…We use the following discrete approximations for the right hand side of Eq. ( 1) as used by Namjoo and Zibaei [54]:…”

Section: Nsfd1 Schemementioning

confidence: 99%

Construction and analysis of some nonstandard finite difference methods for the FitzHugh–Nagumo equation

Agbavon

Appadu

2020

Numerical Methods Partial

View full text Add to dashboard Cite

In this work, we construct four versions of nonstandard finite difference schemes in order to solve the FitzHugh–Nagumo equation with specified initial and boundary conditions under three different regimes giving rise to three cases. The properties of the methods such as positivity and boundedness are studied. The numerical experiment chosen is quite challenging due to shock‐like profiles. The performance of the four methods is compared by computing L1, L∞ errors, rate of convergence with respect to time and central processing unit time at given time, T = 0.5. Error estimates have also been studied for the most efficient scheme.

show abstract

Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes

Cited by 20 publications

References 26 publications

Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization

Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization

Exact and nonstandard finite difference schemes for the Burgers equationB(2,2)

Construction and analysis of some nonstandard finite difference methods for the FitzHugh–Nagumo equation

Contact Info

Product

Resources

About