Use Euler's method with each of the following step sizes to estimate the value of y(1.6), where y is the solution of the initial-value problem y' = y, y(0) = 2. (i) h = 1.6 (ii) h = 0.8 (iii) h = 0.4 find the estimates (i) h = 1.6 y(1.6) = (ii) h = 0.8 y(1.6) = (iii) h = 0.4 y(1.6) =
Use Euler's method with each of the following step sizes to estimate the value of y(1.6), where y is the solution of the initial-value problem y' = y, y(0) = 2. (i) h = 1.6 (ii) h = 0.8 (iii) h = 0.4 find the estimates (i) h = 1.6 y(1.6) = (ii) h = 0.8 y(1.6) = (iii) h = 0.4 y(1.6) =
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
Use Euler's method with each of the following step sizes to estimate the value of y(1.6), where y is the solution of the initial-value problem y' = y, y(0) = 2.
(i) h = 1.6
(ii) h = 0.8
(iii) h = 0.4
find the estimates
(i) h = 1.6
(ii) h = 0.8
(iii) h = 0.4
(ii) h = 0.8
(iii) h = 0.4
find the estimates
(i) h = 1.6
y(1.6) =
(ii) h = 0.8
y(1.6) =
(iii) h = 0.4
y(1.6) =
part C
Since the solution to y' = y is y = 2ex, the exact value of y(1.6) is 2e1.6.
Thus, rounding to four decimal places, when h = 1.6, the error is
part C
Since the solution to y' = y is y = 2ex, the exact value of y(1.6) is 2e1.6.
Thus, rounding to four decimal places, when h = 1.6, the error is
(exact) − (approximate) = 2e1.6 − 5.2 =
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