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Differential Equations Lecture Work Solutions 293

Differential Equations Lecture Work Solutions 293 - 2 f(x =...

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2. f ( x ) = e x x = . 1 Approximate f ( x ) at x = 2 using forward difference f (2) f (2 + . 1) f (2) . 1 + O ( . 1) f (2) e 2 . 1 e 2 . 1 = 7 . 7711381 Approximate f ( x ) at x = 2 using centered difference f (2) f (2 + . 1) f (2 . 1) . 2 + O ( . 1 2 ) f (2) e 2 . 1 e 1 . 9 . 2 = 7 . 40137735 Approximate f ( x ) at x = 2 using second order three point f (2) f (2 + . 2) + 4 f (2 + . 1) 3 f (2) . 2 + O ( . 1 2 ) f (2) e 2 . 2 + 4 e 2 . 1 3 e 2 . 2 = 7 . 36248927 Exact answer f (2) = e 2 = 7 . 3890560989 . . . O ( . 1) O ( . 1 2 ) O ( . 1) 2 Forward Centered 3-point approximate 7.7711381 7.40137735 7.36248927 exact 7.3890560989 7.3890560989 7.3890560989
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