NUMERICAL SOLUTIONS FOR THE FOURTH ORDER EXTENDED FISHER-KOLMOGOROV EQUATION WITH HIGH ACCURACY BY DIFFERENTIAL QUADRATURE METHOD

Bashan A., UÇAR Y., YAĞMURLU N. M., ESEN A.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, cilt.9, sa.3, ss.273-284, 2018 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 3
  • Basım Tarihi: 2018
  • Dergi Adı: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
  • Sayfa Sayıları: ss.273-284
  • Anahtar Kelimeler: Partial differential equations, differential quadrature method, EFK equation, modified cubic B-Splines, CUBIC B-SPLINES, MARGINAL STABILITY, PROPAGATING FRONTS, UNSTABLE STATES
  • İnönü Üniversitesi Adresli: Evet

Özet

In this paper, modified cubic B-spline based differential quadrature method (MCB-DQM) has been used to obtain the numerical solutions for the fourth order extended Fisher-Kolmogorov equation (EFK). After using DQM for discretization of the EFK equation, ordinary differential equation systems have been obtained. For time integration, strong stability preserving Runge-Kutta method has been used. Numerical solutions of the three test problems have been investigated. The efficiency and accuracy of the method have been measured by calculating error norms L-2 and L-infinity. The present obtained numerical results have been compared with the published numerical results and the comparison has shown that the method is an effective numerical scheme to solve the EFK equation.