Consider the linear problem Y' (t) = XY (t) + (1 - A) cos(t) – (1 + X) sin(t), Y(0) = 1. The true solution is Y(t) = sin(t) + cos(t). Solve this problem using Euler's method with several values of λ and h, for 0 ≤ t ≤ 10. Comment on the results. (a) λ = -1; h = 0.5, 0.25, 0.125.
Consider the linear problem Y' (t) = XY (t) + (1 - A) cos(t) – (1 + X) sin(t), Y(0) = 1. The true solution is Y(t) = sin(t) + cos(t). Solve this problem using Euler's method with several values of λ and h, for 0 ≤ t ≤ 10. Comment on the results. (a) λ = -1; h = 0.5, 0.25, 0.125.
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
![3. Consider the linear problem
Y'(t) = XY(t) + (1 - A) cos(t) – (1 + X) sin(t), Y(0) = 1.
The true solution is Y(t) = sin(t) + cos(t). Solve this problem using Euler's
method with several values of A and h, for 0 ≤ t ≤ 10. Comment on the
results.
Created with
-1; h = 0.5, 0.25, 0.125.
(a) A =
(b) = 1; h= 0.5, 0.25, 0.125.
(c) A = -5; h = 0.5, 0.25, 0.125, 0.0625.
(d) λ = 5; h = 0.125, 0.0625.
25,0,125,00625Screen Reco](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f415121-4206-4bd3-908f-4fe8a9624f99%2Ff0be36e8-36c7-4d95-9b0c-364e2b00011b%2F751uwv_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider the linear problem
Y'(t) = XY(t) + (1 - A) cos(t) – (1 + X) sin(t), Y(0) = 1.
The true solution is Y(t) = sin(t) + cos(t). Solve this problem using Euler's
method with several values of A and h, for 0 ≤ t ≤ 10. Comment on the
results.
Created with
-1; h = 0.5, 0.25, 0.125.
(a) A =
(b) = 1; h= 0.5, 0.25, 0.125.
(c) A = -5; h = 0.5, 0.25, 0.125, 0.0625.
(d) λ = 5; h = 0.125, 0.0625.
25,0,125,00625Screen Reco
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