A numerical method for determining the localized initial condition in the FitzHugh-Nagumo and Aliev-Panfilov models

Pavel’chak, I. A.

doi:10.3103/s0278641911030071

Cited by 6 publications

(2 citation statements)

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“…, 2008) and the FitzHugh–Nagumo model for analyzing various processes in the myocardium (Jhangeer et al. , 2021; Pavel’chak, 2011; Yasin et al. , 2022).…”

Section: Introductionmentioning

confidence: 99%

“…Turing systems appear in various biological systems, such as patterns in fish, butterflies, lady bugs, tumor growth and synthetic bacterial population (Shin et al, 2014). We can mention the Gierer-Meinhardt model for pattern formation of spatial tissue structures in morphogenesis (Gierer and Meinhardt, 1972), the morphodynamic (limit) model in describing the cell dynamics and the chemical processes during limb bud formation (Alber et al, 2008) and the FitzHugh-Nagumo model for analyzing various processes in the myocardium (Jhangeer et al, 2021;Pavel'chak, 2011;Yasin et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

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A reduced-order Jacobi spectral collocation method for solving the space-fractional FitzHugh–Nagumo models with application in myocardium

Abbaszadeh,

Bagheri Salec,

Kamel Abd Al-Khafaji

2023

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PurposeThe space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.Design/methodology/approachThe fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.FindingsA fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.Originality/valueThe spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.

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“…, 2008) and the FitzHugh–Nagumo model for analyzing various processes in the myocardium (Jhangeer et al. , 2021; Pavel’chak, 2011; Yasin et al. , 2022).…”

Section: Introductionmentioning

confidence: 99%