Tailored Finite Point Method for Parabolic Problems
2016 ◽
Vol 16
(4)
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pp. 543-562
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Keyword(s):
AbstractIn this paper, we propose a class of new tailored finite point methods (TFPM) for the numerical solution of parabolic equations. Our finite point method has been tailored based on the local exponential basis functions. By the idea of our TFPM, we can recover all the traditional finite difference schemes. We can also construct some new TFPM schemes with better stability condition and accuracy. Furthermore, combining with the Shishkin mesh technique, we construct the uniformly convergent TFPM scheme for the convection-dominant convection-diffusion problem. Our numerical examples show the efficiency and reliability of TFPM.
2010 ◽
Vol 47
(2)
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pp. 198-215
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2016 ◽
Vol 19
(5)
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pp. 1357-1374
2010 ◽
Vol 44
(1)
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pp. 108-108
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2010 ◽
Vol 43
(2)
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pp. 239-260
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2011 ◽
Vol 10
(1)
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pp. 161-182
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2012 ◽
Vol 82
(281)
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pp. 213-226
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2021 ◽
Vol 97
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pp. 298-313
2021 ◽
Vol 182
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pp. 535-554