Abstract
Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary convection-diffusion equations, which are based on use of new variables. Also, we consider these equations in the form of convection-diffusion-reaction and construct unconditionally stable schemes when explicit-implicit approximations are used with splitting of the reaction operator.
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References
Morton, K.W., Kellogg, R.B.: Numerical solution of convection-diffusion problems. Chapman & Hall, London (1996)
Hundsdorfer, W.H., Verwer, J.G.: Numerical solution of time-dependent advection-diffusion-reaction equations. Springer, Berlin (2003)
Samarskii, A.A.: The theory of difference schemes. CRC Press (2001)
Samarskii, A.A., Matus, P.P., Vabishchevich, P.N.: Difference schemes with operator factors. Kluwer, Dordrecht (2002)
Samarskii, A.A., Vabishchevich, P.N.: Computational Heat Transfer. Wiley, Chichester (1995)
Mickens, R.E.: Nonstandard Finite Difference Schemes for Differential Equations. Journal of Difference Equations and Applications 8(9), 823–847 (2002)
Vabishchevich, P.N., Vasilyeva, M.V.: Explicit-implicit schemes for convection-diffusion-reaction problems. Numerical Analisis and Application 5(1), 297–306 (2012)
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Afanasyeva, N., Vabishchevich, P.N., Vasilyeva, M. (2013). Unconditionally Stable Schemes for Non-stationary Convection-Diffusion Equations. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_14
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DOI: https://doi.org/10.1007/978-3-642-41515-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41514-2
Online ISBN: 978-3-642-41515-9
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