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Show that f(z)dr: S(#2-2) +4f(r2i-1) + f(#2)]- an"(c.)} m-1 h4 (0) +2f(2) + 4f(*2-1) + f(*) I80(6 - a)f(4)(c) i=1 i=1

Show that f(z)dr: S(#2-2) +4f(r2i-1) + f(#2)]- an"(c.)} m-1 h4 (0) +2f(2) + 4f(*2-1) + f(*) I80(6 - a)f(4)(c) i=1 i=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Simpson's Rule, we have 2 h | = S (*0) + 4f(r1) + f(r2)] 90 20 where there are three nodes: To, 1; and 12. where c in (xo, r2). Consider the composite Simpson's Rule using n = 2m, h = 4, T; = a + ih, i = 0, 1, 2, .. , 2m. %3! Show that m f(x)dr = E (2-2) + 4f(#2i-1) + f(x2.)] – 90 i=1 m-1 = f (r0) + 2f(72.) + 4f(r2-1) + f(x) 180- h4 3-a)f(4) (c) i=1 i=1 The question of numerical integration based on interpolation. Thank you!
Transcribed Image Text:Simpson's Rule, we have 2 h | = S (*0) + 4f(r1) + f(r2)] 90 20 where there are three nodes: To, 1; and 12. where c in (xo, r2). Consider the composite Simpson's Rule using n = 2m, h = 4, T; = a + ih, i = 0, 1, 2, .. , 2m. %3! Show that m f(x)dr = E (2-2) + 4f(#2i-1) + f(x2.)] – 90 i=1 m-1 = f (r0) + 2f(72.) + 4f(r2-1) + f(x) 180- h4 3-a)f(4) (c) i=1 i=1 The question of numerical integration based on interpolation. Thank you!
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