Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 5. The analytic solution

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Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 5. The analytic solution is

(a) Find a formula involving c and h for the local truncation error in the nth step if the RK4 method is used.

(b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5).

(c) Approximate y(1.5) using the RK4 method with h = 0.1 and h [1] 0.05. See Problem 3. You will need to carry more than six decimal places to see the effect of reducing the step size.

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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' = 2x - 3y + 1, y(1) = 5. The analytic solution

Question:

38 -3(x-1)

Step by Step Answer:

Here the equation is y2x3y1 y1 5 Analytic solution is 12 yx 38 c x 93 9 3x1 a Now ...View the full answer

A First Course in Differential Equations with Modeling Applications

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