On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations

Inci Cilingir Sungu, (Ondokuz Mayıs Üniversitesi, Eğitim Fakültesi, Matematik Eğitimi Bölümü, Samsun, Türkiye)
Emre AYDIN (Ondokuz Mayıs Üniversitesi, Lisansüstü Eğitim Enstitüsü, Matematik Bölümü, Samsun, Türkiye)
Turkish Journal of Mathematics
6 0
Yıl: 2022 Cilt: 46 Sayı: 7 Sayfa Aralığı: 2806 - 2818 Metin Dili: İngilizce DOI: 10.55730/1300-0098.3302 İndeks Tarihi: 12-12-2022

On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations

Öz:
In this study, standard and non-standard finite-difference methods are proposed for numerical solutions of the time-spatial fractional generalized Newell-Whitehead-Segel equations describing the dynamical behavior near the bifurcation point of the Rayleigh-Benard convection of binary fluid mixtures. The numerical solutions have been found for high values of p which shows the degree of nonlinear terms in the equations. The stability and convergence conditions of the obtained difference schemes are determined for each value of p . Errors of methods for various values of p are given in tables. The compatibility of exact solutions and numerical solutions and the effectiveness of the methods are interpreted with the help of tables and graphics. It can be said that not only standard and non-standard finite-difference methods are feasible and effective methods to solve the given equation numerically but also useful in terms of computational cost and memory.
Anahtar Kelime: Generalized Newell-Whitehead-Segel equation (GNWS) Standard Finite-Difference method (SFDM) Non- Standard Finite-Difference method (NSFDM) CFL conditions

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA Cilingir Sungu I, AYDIN E (2022). On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. , 2806 - 2818. 10.55730/1300-0098.3302
Chicago Cilingir Sungu Inci,AYDIN Emre On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. (2022): 2806 - 2818. 10.55730/1300-0098.3302
MLA Cilingir Sungu Inci,AYDIN Emre On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. , 2022, ss.2806 - 2818. 10.55730/1300-0098.3302
AMA Cilingir Sungu I,AYDIN E On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. . 2022; 2806 - 2818. 10.55730/1300-0098.3302
Vancouver Cilingir Sungu I,AYDIN E On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. . 2022; 2806 - 2818. 10.55730/1300-0098.3302
IEEE Cilingir Sungu I,AYDIN E "On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations." , ss.2806 - 2818, 2022. 10.55730/1300-0098.3302
ISNAD Cilingir Sungu, Inci - AYDIN, Emre. "On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations". (2022), 2806-2818. https://doi.org/10.55730/1300-0098.3302
APA Cilingir Sungu I, AYDIN E (2022). On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. Turkish Journal of Mathematics, 46(7), 2806 - 2818. 10.55730/1300-0098.3302
Chicago Cilingir Sungu Inci,AYDIN Emre On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. Turkish Journal of Mathematics 46, no.7 (2022): 2806 - 2818. 10.55730/1300-0098.3302
MLA Cilingir Sungu Inci,AYDIN Emre On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. Turkish Journal of Mathematics, vol.46, no.7, 2022, ss.2806 - 2818. 10.55730/1300-0098.3302
AMA Cilingir Sungu I,AYDIN E On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. Turkish Journal of Mathematics. 2022; 46(7): 2806 - 2818. 10.55730/1300-0098.3302
Vancouver Cilingir Sungu I,AYDIN E On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations. Turkish Journal of Mathematics. 2022; 46(7): 2806 - 2818. 10.55730/1300-0098.3302
IEEE Cilingir Sungu I,AYDIN E "On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations." Turkish Journal of Mathematics, 46, ss.2806 - 2818, 2022. 10.55730/1300-0098.3302
ISNAD Cilingir Sungu, Inci - AYDIN, Emre. "On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations". Turkish Journal of Mathematics 46/7 (2022), 2806-2818. https://doi.org/10.55730/1300-0098.3302
Sayfa Oluşturulma Tarihi
24-04-2024 4:53

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