Differential Equations Lecture Work Solutions 294

Differential Equations Lecture Work Solutions 294 - x is...

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f 0 (2) e 2 . 2 e 1 . 8 . 2 =7 . 438415087 Approximate f 0 ( x )at x = 2 using second order three point f 0 (2) f (2 + . 4) + 4 f (2 + . 2) 3 f (2) . 4 + O ( . 1 2 ) f 0 (2) e 2 . 4 +4 e 2 . 2 3 e 2 . 4 =7 . 2742733 O ( . 2) O ( . 2 2 ) O ( . 2) 2 Forward Centered 3-point approximate 8.179787 7.438415087 7.2742733 exact 7.3890560989 7.3890560989 7.3890560989 diference .7907309 .0493589 -.01147827 .2 . 2 2 . 2 2 The ratio o± errors in ±orward diference was cut by a ±actor o± 2 when the ∆
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Unformatted text preview: x is halved, or the second order approximation, the error was cut by 4 (= 2 2 ) when x is halved. So this is a relatively reliable guide. 294...
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