Newell-Whitehead Denkleminin Çözümü için Yeni Bir Sayısal Yaklaşım

Year 2023, Volume: 23 Issue: 6, 1428 - 1433, 28.12.2023

Derya Yıldırım Sucu Seydi Battal Gazi Karakoç

https://doi.org/10.35414/akufemubid.1323548

Abstract

Bu çalışmada Newell-Whitehead denkleminin sayısal çözümleri kollokasyon yöntemi ile elde edilmiştir. Daha yüksek dereceli fonksiyonlar daha iyi yaklaşımlar ürettiğinden, analiz ve yaklaşım için septik B-spline baz fonksiyonları kullanılmıştır. Mevcut yöntemin yeterliliği ve etkinliği için hata normları hesaplanmıştır. Koşulsuz kararlılık, Von-Neumann teorisi kullanılarak kanıtlanmıştır. Sayısal sonuçlar elde edilmiş ve yapılan karşılaştırmalar tablolar halinde sunulmuştur. Ek olarak, çözümün sayısal davranışını göstermek için tüm sayısal sonuçların grafikleri çizilmiştir. Sayısal sonuçlar, yöntemi daha uygun hale getirir ve doğrusal olmayan çözüm sürecini sistematik olarak ele alır. Bulunan sayısal çözümler, kollokasyon yöntemini Fitzhugh-Nagumo tipi denklemlerin çözümü için oldukça ilgi çekici ve güvenilir kılmaktadır.

Keywords

Fitzhugh-Nagumo denklemi, Newell-Whitehead denklemi, kollokasyon, sonlu elemanlar yöntemi, septik B-spline

A Novel Numerical Approach for Solving the Newell-Whitehead Equation

Abstract

Numerical solutions of Newell-Whitehead equation are investigated by collocation method in this study. Since higher order functions produce better approximations, septic B-spline basis functions is used for analysis and approximation. Error norms are calculated for the adequacy and effectiveness of the current method. Unconditional stability is proved using Von-Neumann theory. The numerical results are obtained and the comparisons are presented in the tables. Additionally, simulations of all numerical results are plotted to show the numerical behavior of the solution. Numerical results make the method more convenient and systematically handle the nonlinear solution process. The numerical solutions found make the method attractive and reliable for the solution of Fitzhugh-Nagumo type equations.

Keywords

Fitzhugh-Nagumo equation, Newell-Whitehead equation, collocation, finite element, septic B-spline

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