Consider the following nonlinear boundary value problem f" = f³ - ff', vith 1 ≤ x ≤ 2, f(1) = 1/2, and f(2)= 1/3. (a) Find the actual solution f(x). (h). Use the direct method co colution
Consider the following nonlinear boundary value problem f" = f³ - ff', vith 1 ≤ x ≤ 2, f(1) = 1/2, and f(2)= 1/3. (a) Find the actual solution f(x). (h). Use the direct method co colution
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
![Consider the following nonlinear boundary value problem
f" = f³ - ff',
(1)
with 1 ≤ x ≤ 2, f(1) = 1/2, and f(2)= 1/3.
(a) Find the actual solution f(x).
(b) Use the direct method to approximate the solution to (1). Plot the error norm
|| || versus h = {10-¹, 10-2,..., 10-5} on a log-log scale for each fixed number
of iterations N = {10¹, 10²,...1
. 105}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed051053-4bf3-451a-ac87-e1db40d07cdc%2F97cd5c41-a924-4d9a-be0e-9328ff9bcd82%2Fzefdhhx_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following nonlinear boundary value problem
f" = f³ - ff',
(1)
with 1 ≤ x ≤ 2, f(1) = 1/2, and f(2)= 1/3.
(a) Find the actual solution f(x).
(b) Use the direct method to approximate the solution to (1). Plot the error norm
|| || versus h = {10-¹, 10-2,..., 10-5} on a log-log scale for each fixed number
of iterations N = {10¹, 10²,...1
. 105}.
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