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Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems

Author

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  • P. G. Dlamini
  • S. S. Motsa
  • M. Khumalo

Abstract

We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss‐Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller‐box method.

Suggested Citation

  • P. G. Dlamini & S. S. Motsa & M. Khumalo, 2013. "Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:941096
    DOI: 10.1155/2013/941096
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    References listed on IDEAS

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    1. Bertram Düring & Michel Fournié & Ansgar Jüngel, 2003. "High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 767-789.
    2. S. S. Motsa & P. G. Dlamini & M. Khumalo, 2012. "Solving Hyperchaotic Systems Using the Spectral Relaxation Method," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, December.
    3. S. S. Motsa & P. G. Dlamini & M. Khumalo, 2012. "Solving Hyperchaotic Systems Using the Spectral Relaxation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Hayat, T. & Abbas, Z., 2008. "Heat transfer analysis on the MHD flow of a second grade fluid in a channel with porous medium," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 556-567.
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