HIGH-ORDER FINITE DIFFERENCE SCHEMES FOR SOLVING THE ADVECTION-DIFFUSION EQUATION
MATHEMATICAL & COMPUTATIONAL APPLICATIONS, cilt.15, sa.3, ss.449-460, 2010 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 15 Sayı: 3
- Basım Tarihi: 2010
- Dergi Adı: MATHEMATICAL & COMPUTATIONAL APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.449-460
- Yıldız Teknik Üniversitesi Adresli: Hayır
Özet
Up to tenth-order finite difference schemes are proposed in this paper to solve one-dimensional advection-diffusion equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order finite difference schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. The methods are implemented to solve two problems having exact solutions. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the current methods. The techniques are seen to be very accurate in solving the advection-diffusion equation for Pe <= 5. The produced results are also seen to be more accurate than some available results given in the literature.