# 560E619B484E9F7E04DADA115B4A154F.jpg - 10 Own 1 1 2 20 wij...

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Unformatted text preview: 10 - Own - 1. 1 + ( 2 + 20) wij - Owit 1, 1 = Ow1 - 1. 1 - 1 + ( 2 - 20 ) wi, 1 - 1 + o with, j - 1 . which leads to the template shown in Figure 8.7 . i - I i i + 1 Figure 8. 7 Mesh points for Crank - Nicolson Method . At each time step , the open circles are the unknowns and the filled circles are known from the previous step . Set wj = [ wij . .... Wmil' . In matrix form , the Crank - Nicolson Method is AW; = BW ; - 1 + 0 ( \$ ; - 1 + 5; ). where `2 + 20 - 0 O - OJ 2 + 20 - 0 A = - IJ 2 + 20 - IT U - IT 2 + 20 | 2 - 20 2 - 20 B = O 2 - 20 2 - 20 and s ; = [ woj . O . .... O. wn+ 1. 1\' . Applying Crank - Nicolson to the heat equation gives the...
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• One '14
• Heat, Figure 8, matrix form, Nicolson Method

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