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Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation

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  • Zahari Zlatev
  • Ivan Dimov
  • István Faragó
  • Krassimir Georgiev
  • Ã gnes Havasi
  • Tzvetan Ostromsky

Abstract

Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples.

Suggested Citation

  • Zahari Zlatev & Ivan Dimov & István Faragó & Krassimir Georgiev & à gnes Havasi & Tzvetan Ostromsky, 2011. "Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-16, December.
    • Handle: RePEc:hin:jnijde:520840
    DOI: 10.1155/2011/520840
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