Stability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives |
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Authors: | Cui-cui Ji Rui Du |
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Affiliation: | School of Mathematics, Southeast University, Nanjing, China |
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Abstract: | ABSTRACTWe present second-order difference schemes for a class of parabolic problems with variable coefficients and mixed derivatives. The solvability, stability and convergence of the schemes are rigorously analysed by the discrete energy method. Using the Richardson extrapolation technique, the fourth-order accurate numerical approximations both in time and space are obtained. It is noted that the Richardson extrapolation algorithms can preserve stability of the original difference scheme. Finally, numerical examples are carried out to verify the theoretical results. |
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Keywords: | Parabolic equation mixed derivatives variable coefficients finite difference scheme stability convergence Richardson extrapolation |
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