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2. Please use the following data to calculate f(7) via linear, quadratic, cubic and quartic interpolation. 2.5 3.5 7.5 10 12.5 15 17.5 f(x) 13 11 8.5 8.2 6.2 5.2 4.8 4.8

2. Please use the following data to calculate f(7) via linear, quadratic, cubic and quartic interpolation. 2.5 3.5 7.5 10 12.5 15 17.5 f(x) 13 11 8.5 8.2 6.2 5.2 4.8 4.8

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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Please solve question 2.
1. An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25x² where V is the shear force and x is length in distance along the beam. We know that V = dM/dx, and M is the bending moment. Integration yields the relationship M = M, + Vdx If Mo is zero and x 12, calculate M using a) trapezoidal rule with 1 m stepsize b) Simpson's 1/3 rule with 1 m stepsize c) Simpson's 3/8 rule with I m stepsize. 2. Please use the following data to calculate f (7) via linear, quadratic, cubic and quartic interpolation. 2.5 3.5 5 6 7.5 10 12.5 15 17.5 f(x) 13 11 8.5 8.2 7 6.2 5.2 4.8 4.8 3. Please use the following dața to calculate f (x = 4.5, y = 3.2) via bilinear interpolation. x = 2 90.00 |x = 8 x = 0 100.00 x = 4 80.00 r= 6 y = 0 70.00 60.00 53.50 y = 2 y = 4 y = 6 85.00 64.49 48.15 50.00 70.00 55.00 48.90 38.78 38.43 30.39 35.03 27.07 25.00 40.00 30.00 20.00 y = 8 40.00 35.00 30.00 4. Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where y(0) = 1. dy = (1 + 2x)/y dx a) Euler's method b) Heun's method without the corrector. 80 ODII DD 000 F3 F4 F5 F6 F7 F8 F9 F #3 2$ & * 70 3 5 7 8 9 < CO
Transcribed Image Text:1. An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25x² where V is the shear force and x is length in distance along the beam. We know that V = dM/dx, and M is the bending moment. Integration yields the relationship M = M, + Vdx If Mo is zero and x 12, calculate M using a) trapezoidal rule with 1 m stepsize b) Simpson's 1/3 rule with 1 m stepsize c) Simpson's 3/8 rule with I m stepsize. 2. Please use the following data to calculate f (7) via linear, quadratic, cubic and quartic interpolation. 2.5 3.5 5 6 7.5 10 12.5 15 17.5 f(x) 13 11 8.5 8.2 7 6.2 5.2 4.8 4.8 3. Please use the following dața to calculate f (x = 4.5, y = 3.2) via bilinear interpolation. x = 2 90.00 |x = 8 x = 0 100.00 x = 4 80.00 r= 6 y = 0 70.00 60.00 53.50 y = 2 y = 4 y = 6 85.00 64.49 48.15 50.00 70.00 55.00 48.90 38.78 38.43 30.39 35.03 27.07 25.00 40.00 30.00 20.00 y = 8 40.00 35.00 30.00 4. Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where y(0) = 1. dy = (1 + 2x)/y dx a) Euler's method b) Heun's method without the corrector. 80 ODII DD 000 F3 F4 F5 F6 F7 F8 F9 F #3 2$ & * 70 3 5 7 8 9 < CO
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