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Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters

Author

Listed:
  • Gurhan Gurarslan

    (Department of Civil Engineering, Pamukkale University, Denizli 20160, Turkey)

Abstract

A high-accuracy numerical method based on a sixth-order combined compact difference scheme and the method of lines approach is proposed for the advection–diffusion transport equation with variable parameters. In this approach, the partial differential equation representing the advection-diffusion equation is converted into many ordinary differential equations. These time-dependent ordinary differential equations are then solved using an explicit fourth order Runge–Kutta method. Three test problems are studied to demonstrate the accuracy of the present methods. Numerical solutions obtained by the proposed method are compared with the analytical solutions and the available numerical solutions given in the literature. In addition to requiring less CPU time, the proposed method produces more accurate and more stable results than the numerical methods given in the literature.

Suggested Citation

  • Gurhan Gurarslan, 2021. "Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters," Mathematics, MDPI, vol. 9(9), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1027-:d:547607
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    References listed on IDEAS

    as
    1. Gurhan Gurarslan & Halil Karahan & Devrim Alkaya & Murat Sari & Mutlu Yasar, 2013. "Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, April.
    2. Korkmaz, Alper & Dağ, Idris, 2016. "Quartic and quintic B-spline methods for advection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 208-219.
    3. Gurhan Gurarslan, 2014. "Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, April.
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