Good day everybody!(adsbygoogle = window.adsbygoogle || []).push({});

In my Numerical Methods textbook (Applied Numerical Analysis, 7ed, Gerald and Wheatley) the authors derive two equations for the ADI method to be used in an iteration scheme. For row-wise traversions, they get

[tex]uO^{(k+1)}=uO^{(k)}+\rho(uL-2uO+uR)^{(k+1)}+\rho(uA-2uO+uB)^{(k)}[/tex]

and for column-wise traversions

[tex]uO^{(k+2)}=uO^{(k+1)}+\rho(uA-2uO+uB)^{(k+2)}+\rho(uL-2uO+uR)^{(k+1)}[/tex]

Where u represents the nodes, A, B, L, R are above, below, left and right respectively, O is the node in the centre (current), k represents the iteration and rho is an acceleration factor.

I understand that we alternate between these equations for successive iterations (hence the name ) but what I don't get is that it seems to me that the value we're trying to calculate is dependent on itself, e.g how do we determine [tex]uO^{(k+1)}[/tex] if we don't yet have [tex](uL-2uO+uR)^{(k+1)}[/tex] ?

Any insight will be greatly appreciated!

phyz

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The Alternating Direction Implicit Method in 2-D

Loading...

Similar Threads - Alternating Direction Implicit | Date |
---|---|

Mehrstellenverfahren for different grid spacing along the three space directions | Oct 13, 2014 |

Direction field of y'=cos(πx) | Dec 13, 2013 |

Direction of trajectory, system of DE's and portrait phase in plane phase | Oct 24, 2012 |

Seperation of variables / Alternative method to solve a DE | Dec 4, 2009 |

Alternatives to Taylor's book? | Nov 12, 2007 |

**Physics Forums - The Fusion of Science and Community**