# High order compact finite difference

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 February 10, 2004, 05:51 High order compact finite difference #1 Mikhail Guest   Posts: n/a Hallo CFD people I have some problem, may be someone who has expertise in high order compact finite differences (hcfd for short) can help me. Consider 1D stationary convection-diffusion eq. after applying hcfd to it, you get Ax=b, where A is 3x3 block matrix and x=(u'',u',u)'. Matrix A is generally ill-conditioned, but this is not the question of today Now consider time-dependent 1D convection-diffusion eq. In all papers I've read (starting from Lele's paper) they all consider u (the function value ) to be known and at each step solve something like (for the first derivative) Au'=Bu, with A and B - nice tri (or penta) diagonal matrices. So the question is where they get u??? from previous time step or where???? Thanks a lot in advance to all who will answer

 February 11, 2004, 01:06 Re: High order compact finite difference #2 agg Guest   Posts: n/a Yes u will be from previous time step

 February 16, 2004, 00:25 Re: High order compact finite difference #3 Apurva Guest   Posts: n/a Hi Look for Sanjiva Lele's paper in Journal of Computational Physics. Hope it helps Apurva

 February 16, 2004, 00:31 Re: High order compact finite difference #4 Apurva Guest   Posts: n/a try Google Search "compact higher order" + "finite difference" It will help Apurva Shukla