Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = xy + Vy, y(0) = 1; y(0.5) y(0.5) = y(0.5) = (h = 0.1) |(h = 0.05)

Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = xy + Vy, y(0) = 1; y(0.5) y(0.5) = y(0.5) = (h = 0.1) |(h = 0.05)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

TEAC
Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.
y' = xy + y, y(0) = 1; y(0.5)
y(0.5) =
(h = 0.1)
y(0.5) z
(h = 0.05)
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Expert Solution

Step 1

To find- Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then h = 0.05

$y' = x y + \sqrt{y}, y (0) = 1; y (0.5)$

Method Used-

Improved Euler's Method

$y_{n + 1} = y_{n} + \frac{h}{2} (f (x_{n}, y_{n}) + f (x_{n + 1}, {\bar{y}}_{n + 1})) where {\bar{y}}_{n + 1} = y_{n} + h f (x_{n}, y_{n}) x_{n + 1} = x_{n} + h$