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Get Full Access to Numerical Analysis - 9 Edition - Chapter 5.3 - Problem 10
Get Full Access to Numerical Analysis - 9 Edition - Chapter 5.3 - Problem 10

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Solved: Given the initial-value problem y = 1 t2 y t y2 , 1 t 2, y(1) = 1, with exact

ISBN: 9780538733519 459

Solution for problem 10 Chapter 5.3

Numerical Analysis | 9th Edition

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Problem 10

Given the initial-value problem y = 1 t2 y t y2 , 1 t 2, y(1) = 1, with exact solution y(t) = 1/t: a. Use Taylors method of order two with h = 0.05 to approximate the solution, and compare it with the actual values of y. b. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual values. i. y(1.052) ii. y(1.555) iii. y(1.978) c. Use Taylors method of order four with h = 0.05 to approximate the solution, and compare it with the actual values of y. d. Use the answers generated in part (c) and piecewise cubic Hermite interpolation to approximate the following values of y, and compare them to the actual values. i. y(1.052) ii. y(1.555) iii. y(1.978)

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MATH 340 – INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS What We Covered: April 4 1. Course Content – Chapter 9: Linear Systems with Constant Coefficients a. Section 9.6: The Exponential of a Matrix 1 2 i. The exponential of the matrix A is defined to be = 2! + + 1 3 ∞ 1 3! +...= ∑=0! ii. Proposition: Suppose A is an nxn matrix 1. Then =

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Step 3 of 3

ISBN: 9780538733519

This full solution covers the following key subjects: . This expansive textbook survival guide covers 73 chapters, and 1135 solutions. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 9. Numerical Analysis was written by and is associated to the ISBN: 9780538733519. The answer to “Given the initial-value problem y = 1 t2 y t y2 , 1 t 2, y(1) = 1, with exact solution y(t) = 1/t: a. Use Taylors method of order two with h = 0.05 to approximate the solution, and compare it with the actual values of y. b. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual values. i. y(1.052) ii. y(1.555) iii. y(1.978) c. Use Taylors method of order four with h = 0.05 to approximate the solution, and compare it with the actual values of y. d. Use the answers generated in part (c) and piecewise cubic Hermite interpolation to approximate the following values of y, and compare them to the actual values. i. y(1.052) ii. y(1.555) iii. y(1.978)” is broken down into a number of easy to follow steps, and 136 words. The full step-by-step solution to problem: 10 from chapter: 5.3 was answered by , our top Math solution expert on 03/16/18, 03:30PM. Since the solution to 10 from 5.3 chapter was answered, more than 215 students have viewed the full step-by-step answer.

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