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

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

(a) Approximate y(0.1) using one step and the RK4 method.

(b) Find a bound for the local truncation error in y1.

(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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A First Course in Differential Equations with Modeling Applications

ISBN: 978-1111827052

10th edition

Authors: Dennis G. Zill

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Question Posted: Nov 02, 2020 04:59 AM

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

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a Let h 01 we have fx y 2y x 0 yo 1 With n 0the Rk method is k f xo Yo 2x1 ...View the full answer

A First Course in Differential Equations with Modeling Applications

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