Crank-Nicolson Block-centered Finite Differences Method for Hyperbolic Problems

doi:10.3981/j.issn.1000-7857.2011.09.009

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Science & Technology Review ›› 2011, Vol. 29 ›› Issue (11-09) : 57-61. DOI: 10.3981/j.issn.1000-7857.2011.09.009

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Crank-Nicolson Block-centered Finite Differences Method for Hyperbolic Problems

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Abstract

The Crank-Nicolson block-centered finite difference method studies the solution of the linear hyperbolic differential problems in the bounded domain with sufficiently smooth data. This method is based on both block-center finite difference method and parabolic Crank-Nicolson format. Both the approximate solution and its first derivatives are obtained for all non-uniform grids. Its characteristics are that the approximate solution according to the discrete L2-norm is achieved optimal order error estimation, and the approximate solution of the first derivatives is reached at super convergence error estimation. This method does not increase the calculation. Numerical tests are identical with theoretical analysis; it explains that the format possesses the efficient convergence.

Key words

hyperbolic differential equation / Crank-Nicolson block-centered finite differences method / error estimation

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Crank-Nicolson Block-centered Finite Differences Method for Hyperbolic Problems[J]. Science & Technology Review, 2011, 29(11-09): 57-61 https://doi.org/10.3981/j.issn.1000-7857.2011.09.009