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(b) Given that the exact solution of ni fmi Chapter 3 (3+e" cos(0.5x) dx is 10.2421. Hence, find the 0 relative error for each n for part (a). (c) Give the conclusion in term of accuracy for the answer in part (b).

(b) Given that the exact solution of ni fmi Chapter 3 (3+e" cos(0.5x) dx is 10.2421. Hence, find the 0 relative error for each n for part (a). (c) Give the conclusion in term of accuracy for the answer in part (b).

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 1 a,b,c only. Thank you

(b) Given that the exact solution of 2. Integrate fm 0 (a) Midpoint rule relative error for each n for part (a). (c) Give the conclusion in term of accuracy for the answer in part (b). x√x+3 dx by using the following methods with 6 subintervals. (b) Trapezoidal rule (c) Simpson's rule i fmi Chapter 3 (3+ e* cos(0.5x)) dx is 10.2421. Hence, find the 0 c) 11.1071 Answer 1 a) n=4: 10.2171, n=8: 10.2359, n=12: 10.2392. b) n=4: 0.2441%, n=8: 0.0605%, n=12: 0.0283%. c) The accuracy of the Midpoint rule is higher when the larger number of steps is applied. 2. a) 11.0913 b) 11.1386
Transcribed Image Text:(b) Given that the exact solution of 2. Integrate fm 0 (a) Midpoint rule relative error for each n for part (a). (c) Give the conclusion in term of accuracy for the answer in part (b). x√x+3 dx by using the following methods with 6 subintervals. (b) Trapezoidal rule (c) Simpson's rule i fmi Chapter 3 (3+ e* cos(0.5x)) dx is 10.2421. Hence, find the 0 c) 11.1071 Answer 1 a) n=4: 10.2171, n=8: 10.2359, n=12: 10.2392. b) n=4: 0.2441%, n=8: 0.0605%, n=12: 0.0283%. c) The accuracy of the Midpoint rule is higher when the larger number of steps is applied. 2. a) 11.0913 b) 11.1386
Trapezoidal rule. he has a 1. Use the Midpoint rule to evaluate (a) n = 4, 8, 12. EXERCISES 3.6 IT $(3+e™* cos(0.5x)) dx for 0
Transcribed Image Text:Trapezoidal rule. he has a 1. Use the Midpoint rule to evaluate (a) n = 4, 8, 12. EXERCISES 3.6 IT $(3+e™* cos(0.5x)) dx for 0
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