
Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Textbook Question
Chapter 5.3, Problem 7ES
Repeat Exercise 5 using Taylor’s method of order four.
5. Use Taylor’s method of order two to approximate the solutions for each of the following initial-value problems.
- a. y′ = y/t − (y/t)2, 1 ≤ t ≤ 1.2, y(1) = 1, with h = 0.1
- b. y′ = sin t + e−t, 0 ≤ t ≤ 1, y(0) = 0, with h = 0.5
- c. y′ = (y2 + y)/t, 1 ≤ t ≤ 3, y(1) = −2, with h = 0.5
- d. y′ = −ty + 4ty−1, 0 ≤ t ≤ 1, y(0) = 1, with h = 0.25
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