We consider the following Cauchy problem y '(t) = yt, 0SIS1, y(0) = 0. 1) Prove that the function y is not k-Lipschitz in a neighborhood of 0. 2) Solve the Cauchy problem. 3) Show that the explicit Euler method fails to approximate the non trivial solution of the initial value problem.
We consider the following Cauchy problem y '(t) = yt, 0SIS1, y(0) = 0. 1) Prove that the function y is not k-Lipschitz in a neighborhood of 0. 2) Solve the Cauchy problem. 3) Show that the explicit Euler method fails to approximate the non trivial solution of the initial value problem.
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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![Advanced Math
2&3 please
Exercise 1
We consider the following Cauchy problem
Sy '(t) = yt, 0SIS1,
y(0) =
%3D
0.
%3D
1) Prove that the function y is not k-Lipschitz in a neighborhood of 0.
2) Solve the Cauchy problem.
3) Show that the explicit Euler method fails to approximate the non trivial solution of the initial value
problem.
4) Consider the same problem with the imnlinis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae536901-f783-4263-b044-5b3344420bbf%2F35111b94-1c6b-46cd-b712-7f5c6a2211b9%2Fhky6cn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Advanced Math
2&3 please
Exercise 1
We consider the following Cauchy problem
Sy '(t) = yt, 0SIS1,
y(0) =
%3D
0.
%3D
1) Prove that the function y is not k-Lipschitz in a neighborhood of 0.
2) Solve the Cauchy problem.
3) Show that the explicit Euler method fails to approximate the non trivial solution of the initial value
problem.
4) Consider the same problem with the imnlinis
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