A Survey of the Implementation of Numerical Schemes for Linear Advection Equation

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References

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[2] McRea, G.J. and Godin, W.R. (1967) Numerical Solution of Atmospheric Diffusion for Chemically Reacting Flows. Journal of Computational Physics, 77, 1-42.

[3] Morton, K.W. (1980) Stability of Finite Difference Approximations to a Diffusion-Convection Equation. International Journal for Numerical Methods in Engineering, 15, 677-683.

http://dx.doi.org/10.1002/nme.1620150505

[4] Hundsdorfer, W. and Koren, B. (1995) A Positive Finite-Difference Advection Scheme Applied on Locally Refined Grids. Journal of Computational Physics, 117, 35-36. http://dx.doi.org/10.1006/jcph.1995.1042

[5] Canuto, C. and Hussaini, M. (1988) Spectral Methods in Fluids Dynamics. Springer Series in Computational Physics, Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-642-84108-8

[6] Mitchell, A.R. and Griffiths, D.F. (1980) The Finite Difference Method in Partial Differential Equations. John Wiley & Sons, Chichester.

[7] Mickens, R.E. (2000) Applications of Nonstandard Finite Differences Schemes. World Scientific Publishing, River Edge.

[8] Dehghan, M. (2005) On the Numerical Solution of the One-Dimensional Convection-Diffusion Equation. Mathematical Problems in Engineering, 1, 61-74. http://dx.doi.org/10.1155/MPE.2005.61