A First Course in Differential Equations with Modeling Applications (MindTap Course List)

11th Edition

ISBN: 9781305965720

Author: Dennis G. Zill

Publisher: Cengage Learning

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Differential Equations

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Textbook Question

Chapter 9.1, Problem 13E

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

(a) Approximate y(0.1) using one step and Euler’s 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 Euler’s method.
(e) Verify that the global truncation error for Euler’s method is O(h) by comparing the errors in parts (a) and (d).

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Chapter 9.1, Problem 11E

Chapter 9.1, Problem 14E

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A First Course in Differential Equations with Modeling Applications (MindTap Course List)

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