Consider the initial-value problem y'= 2x - 3y + 1, y(1) = 6. The analytic solution is = + =x + 47 e-3(x-1). 1 2. 9 3 9 (a) Find a formula involving c and h for the local truncation error in the nth step if Euler's method i y(x) 47 h²e-3(c-1) 2 (b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5 0 225
Consider the initial-value problem y'= 2x - 3y + 1, y(1) = 6. The analytic solution is = + =x + 47 e-3(x-1). 1 2. 9 3 9 (a) Find a formula involving c and h for the local truncation error in the nth step if Euler's method i y(x) 47 h²e-3(c-1) 2 (b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5 0 225
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Approximate y(1.5) using h = 0.1 and h = 0.05 with Euler's method
![Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 6. The analytic solution is
y(x) = 1 + x +47e²
e-3(x - 1).
(a) Find a formula involving c and h for the local truncation error in the nth step if Euler's method is
-h²e²
‚—3(c-1)
47
(b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5).
0.235](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe82fa668-1fcd-4b5f-ba57-d40fab71d1eb%2Fa033f3e0-88b7-423c-a67b-94d784e282dc%2Fb6zrp5h_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 6. The analytic solution is
y(x) = 1 + x +47e²
e-3(x - 1).
(a) Find a formula involving c and h for the local truncation error in the nth step if Euler's method is
-h²e²
‚—3(c-1)
47
(b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5).
0.235
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