Differential Equations Lecture Work Solutions 293

Differential - 2 f(x = ex ∆x =.1 Approximate f(x at x = 2 using forward difference f(2 ∼ f(2.1 − f(2 O.1.1 f(2 ∼ e2.1 − e2 = 7.7711381.1

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Unformatted text preview: 2. f (x) = ex ∆x = .1 Approximate f (x) at x = 2 using forward difference f (2) ∼ f (2 + .1) − f (2) + O (.1) .1 f (2) ∼ e2.1 − e2 = 7.7711381 .1 Approximate f (x) at x = 2 using centered difference f (2) ∼ f (2 + .1) − f (2 − .1) + O (.12) .2 f (2) ∼ e2.1 − e1.9 = 7.40137735 .2 Approximate f (x) at x = 2 using second order three point f (2) ∼ −f (2 + .2) + 4f (2 + .1) − 3f (2) + O (.12 ) .2 −e2.2 + 4e2.1 − 3e2 = 7.36248927 f (2) ∼ .2 Exact answer f (2) = e2 = 7.3890560989 . . . O (.1) Forward approximate 7.7711381 exact 7.3890560989 difference .382082037 ∼ .1 O (.12 ) Centered 7.40137735 7.3890560989 .01232125 ∼ .12 O (.1)2 3-point 7.36248927 7.3890560989 -.0265668 ∼ .12 Now use ∆x = .2 Approximate f (x) at x = 2 using forward difference f (2) ∼ f (2 + .2) − f (2) + O (.2) .2 f (2) ∼ e2.2 − e2 = 8.179787 .2 Approximate f (x) at x = 2 using centered difference f (2) ∼ f (2 + .2) − f (2 − .2) + O (.22) .4 293 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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