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

被引:3
作者
Abbaszadeh, Mostafa [1 ]
Salec, AliReza Bagheri [2 ]
Abd Al-Khafaji, Shurooq Kamel [2 ]
机构
[1] Amirkabir Univ Technol, Dept Math & Comp Sci, Tehran, Iran
[2] Univ Qom, Fac Basic Sci, Dept Math, Qom, Iran
关键词
Fractional calculus; FitzHugh-Nagumo models; Proper orthogonal decomposition method; Spectral method; Error estimate; PROPER ORTHOGONAL DECOMPOSITION; ACCURATE NUMERICAL-METHOD; FINITE-VOLUME METHOD; COMPACT ADI SCHEME; DIFFERENTIAL-EQUATIONS; DIFFUSION EQUATION; MESHLESS METHOD; ERROR ESTIMATE; WAVE-EQUATION; TIME;
D O I
10.1108/EC-06-2023-0254
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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.
引用
收藏
页码:2980 / 3008
页数:29
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