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Differential Equations Lecture Work Solutions 307

Differential Equations Lecture Work Solutions 307 - t 2 u...

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u n j +1 = u + ∆ xu x + (∆ x ) 2 2 u xx + (∆ x ) 3 6 u xxx + (∆ x ) 4 24 u xxxx · · · u n j 1 = u xu x + (∆ x ) 2 2 u xx (∆ x ) 3 6 u xxx + (∆ x ) 4 24 u xxxx · · · So u n j +1 2 u n j + u n j 1 2(∆ x ) 2 = 1 2 u xx + (∆ x ) 2 24 u xxxx + · · · The RHS now becomes α ( u xx + t 2 u txx + 1 24 (∆ x ) 2 u xxxx + · · · ) Combine LHS and RHS u t + t 2 u tt + · · · = α ( u xx
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Unformatted text preview: t 2 u txx + 1 24 (∆ x ) 2 u xxxx + ··· ) Thus the truncation error is O (∆ t, (∆ x ) 2 ) Notice that it is only frst order in time. 307...
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