KOLLOKASYON SONLU ELEMAN YÖNTEMİ İLE MKdV DENKLEMİNİN SAYISAL ÇÖZÜMLERİ

Yıl 2018, Cilt: 6 Sayı: 2, 206 - 218, 01.06.2018

Seydi Battal Gazi Karakoc

Öz

Bu çalışmada, modifiye edilmiş Korteweg-de Vries (MKdV) denkleminin sayısal çözümleri septik B-spline kollokasyon sonlu eleman yöntemi kullanılarak elde edilmiştir. Önerilen sayısal algoritmanın doğruluğu, tek soliton dalga, iki ve üç soliton dalganın girişimi gibi üç test probleminin uygulanması ile kontrol edilmiştir. Zamana bağlı Crank Nicolson yaklaşımına dayanan sayısal algoritmamız şartsız olarak kararlıdır. Yeni uygulanan yöntemin performansını kontrol etmek için L2, Lsonsuz , hata normları ile I1,I2 , I3 ve I4 değişmezlerinin değerleri hesaplanmıştır. Elde edilen sayısal sonuçlar literatürde bulunan diğer sonuçlarla karşılaştırılmıştır.

Anahtar Kelimeler

Modifiye edilmiş Korteweg-de Vries denklemi, sonlu eleman yöntemi, kollokasyon, septik B-spline, soliton

NUMERICAL SOLUTIONS OF THE MKdV EQUATION VIA COLLOCATION FINITE ELEMENT METHOD

Öz

In this paper, we have obtained numerical solutions of the modified Korteweg-de Vries (MKdV) equation by using septic B-spline collocation finite element method. The suggested numerical algorithm is controlled by applying three test problems including; single soliton wave, interaction of two and three soliton waves. Our numerical algorithm, attributed to a Crank Nicolson approximation in time, is unconditionally stable. To control the performance of the newly applied method, the error norms L2 ,Lsonsuz and invariants I1 ,I2 ,I3, and I4 have been calculated. The obtained numerical results are compared with some of those available in the literature.

Anahtar Kelimeler

Modified Korteweg-de Vries equation, finite element method, collocation, septic B-spline, soliton

Kaynakça

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