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

SARI M., Gurarslan G., Zeytinoglu A.

MATHEMATICAL & COMPUTATIONAL APPLICATIONS, vol.15, no.3, pp.449-460, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2010
  • Journal Name: MATHEMATICAL & COMPUTATIONAL APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.449-460
  • Yıldız Technical University Affiliated: No

Abstract

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.