Abstract
Two block-centered finite difference schemes are introduced and analyzed to solve parabolic equation with time-dependent diffusion coefficient. One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank–Nicolson scheme with second order accuracy in time increment. Second-order error estimates in spacial meshsize both for the original unknown and its derivatives in discrete L 2 norms are established on non-uniform rectangular grid. Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.
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The work is supported by the National Natural Science Foundation of China Grant No. 91330106, 11171190 and the Research Fund for Doctoral Program of High Education by Station Education Ministry of China No. 20120131110003.
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Rui, H., Pan, H. Block-centered finite difference methods for parabolic equation with time-dependent coefficient. Japan J. Indust. Appl. Math. 30, 681–699 (2013). https://doi.org/10.1007/s13160-013-0114-4
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DOI: https://doi.org/10.1007/s13160-013-0114-4
Keywords
- Block-centered finite difference
- Parabolic equation
- Time-dependent diffusion coefficient
- Numerical analysis