11th Edition

ISBN: 9781337652476

Author: ZILL

Publisher: CENGAGE L

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Textbook Question

Chapter 9.2, Problem 17E

Repeat Problem 16 using the initial-value problem y′ = –2y + x, y(0) = 1. The analytic solution is

y ( x ) = 1 2 x − 1 4 + 5 4 e − 2 x .

16. Consider the initial-value problem y′ = 2y, y(0) = 1. The analytic solution is y(x) = e²^x.

(a) Approximate y(0.1) using one step and the RK4 method.
(b) Find a bound for the local truncation error in y₁.
(c) Compare the error in y₁ with your error bound.
(d) Approximate y(0.1) using two steps and the RK4 method.
(e) Verify that the global truncation error for the RK4 method is O(h⁴) by comparing the errors in parts (a) and (d).

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Chapter 9.2, Problem 16E

Chapter 9.2, Problem 18E

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Chapter 9 Solutions

FIRST COURSE IN DIFF.EQ.-WEBASSIGN

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