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Unformatted text preview: u n +1 j = u n j c t x u n +1 j +1 u n +1 j 1 2 ! As before = 1 i sin k m x or = 1 1 + i sin k m x = 1 i sin k m x 1 + 2 sin 2 k m x Taking absolute value   = Re ( ) 2 + Im ( ) 2 = v u u t 1 (1 + 2 sin 2 k m x ) 2 + 2 sin 2 k m x (1 + 2 sin 2 k m x ) 2 so   = s 1 1 + 2 sin 2 k m x 1 This is always less than or equal 1 since the denominator is larger than numerator. Therefore the method is always stable. 321...
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 Fall '08
 BELL,D

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