HIGH-ORDER FINITE DIFFERENCE SCHEMES FOR SOLVING THE ADVECTION-DIFFUSION EQUATION


SARI M. , Gurarslan G., Zeytinoglu A.

MATHEMATICAL & COMPUTATIONAL APPLICATIONS, cilt.15, ss.449-460, 2010 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 15 Konu: 3
  • Basım Tarihi: 2010
  • Dergi Adı: MATHEMATICAL & COMPUTATIONAL APPLICATIONS
  • Sayfa Sayısı: ss.449-460

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.