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Differential Equations Lecture Work Solutions 332

Differential Equations Lecture Work Solutions 332 - Step 1...

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Step 1: u n +1 / 2 j 1 2 u n j +1 / 2 + u n j 1 / 2 1 2 t + F n j +1 / 2 F n j 1 / 2 x + 1 2 u n j 1 / 2 4 u n j +1 / 2 8 u n j + 8 u n j 1 4 u n j 3 / 2 x 3 + 1 2 u n j +1 / 2 4 u n j +3 / 2 8 u n j +1 + 8 u n j 4 u n j 1 / 2 x 3 = 0 Multiply through by 1 2 t and collect terms Step 1: u n +1 / 2 j 1 2 u n j +1 / 2 + u n j 1 / 2 + 1 2 t x F n j +1 / 2 F n j 1 / 2 + t x 3 u n j 1 / 2 8 u n j + 8 u n j 1 4 u n j 3 / 2 + u n j +1 / 2 4 u n j +3 / 2 8 u n j +1 + 8 u n j = 0 Step 2: u n +1 j u n j + t x F n +1 / 2 j +1 / 2 F n +1 / 2 j 1 / 2 + t x 3 u n j 4 u n j +1 8 u n j +1 / 2 + 8 u n j 1 / 2 4 u n j 1 = 0 Another possibility is to include uu xxx term into F . Let G =
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