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1. Given data x 0 0.1 f(x) 1.0000 1.0000 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0003 1.0024 1.0102 1.0313 1.0778 1.1681 1.3277 a. Use the central difference approach, O(h²), h = 0.2, 4 decimal to estimate f''(0.4) b. Use the central difference approach, O(h²), h = 0.1, 4 decimal to estimate f''(0.4) c. Based on answers (a) and (b), use Richardson's extrapolation with p=2, 4 decimal places, to estimate f''(0.4) d. Use the derivative of quadratic interpolation, 4 decimal places, and the nearest point x=0.3, x=0.5,x=0.6 to estimate f'(0.4)

1. Given data x 0 0.1 f(x) 1.0000 1.0000 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0003 1.0024 1.0102 1.0313 1.0778 1.1681 1.3277 a. Use the central difference approach, O(h²), h = 0.2, 4 decimal to estimate f''(0.4) b. Use the central difference approach, O(h²), h = 0.1, 4 decimal to estimate f''(0.4) c. Based on answers (a) and (b), use Richardson's extrapolation with p=2, 4 decimal places, to estimate f''(0.4) d. Use the derivative of quadratic interpolation, 4 decimal places, and the nearest point x=0.3, x=0.5,x=0.6 to estimate f'(0.4)

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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1. Given data 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x 0.8 f(x) 1.0000 1.0000 1.0003 1.0024 1.0102 1.0313 1.0778 1.1681 1.3277 a. Use the central difference approach, O(h²), h = 0.2, 4 decimal to estimate f''(0.4) b. Use the central difference approach, O(h²), h = 0.1, 4 decimal to estimate f''(0.4) c. Based on answers (a) and (b), use Richardson's extrapolation with p=2, 4 decimal places, to estimate f''(0.4) d. Use the derivative of quadratic interpolation, 4 decimal places, and the nearest point x=0.3, x=0.5,x=0.6 to estimate f''(0.4)
Transcribed Image Text:1. Given data 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x 0.8 f(x) 1.0000 1.0000 1.0003 1.0024 1.0102 1.0313 1.0778 1.1681 1.3277 a. Use the central difference approach, O(h²), h = 0.2, 4 decimal to estimate f''(0.4) b. Use the central difference approach, O(h²), h = 0.1, 4 decimal to estimate f''(0.4) c. Based on answers (a) and (b), use Richardson's extrapolation with p=2, 4 decimal places, to estimate f''(0.4) d. Use the derivative of quadratic interpolation, 4 decimal places, and the nearest point x=0.3, x=0.5,x=0.6 to estimate f''(0.4)
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