2. An initial value problem and its exact solution y(x) are given below. Apply Euler's meu twice to approximate to this solution on the interval [0, ½], first with step size h = 0.25 (two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place values of the two approximations at x = 2 with the value y(½) of the actual solution. y' =(1+ y²), y(0) = 1; y(x) = tan (x + Tt) "exact" approx. Yn+1 f(Xn Yn) h.f(xn Yn) Yn+1 Xn+1 Yn h 1 1 3 4
2. An initial value problem and its exact solution y(x) are given below. Apply Euler's meu twice to approximate to this solution on the interval [0, ½], first with step size h = 0.25 (two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place values of the two approximations at x = 2 with the value y(½) of the actual solution. y' =(1+ y²), y(0) = 1; y(x) = tan (x + Tt) "exact" approx. Yn+1 f(Xn Yn) h.f(xn Yn) Yn+1 Xn+1 Yn h 1 1 3 4
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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![2. An initial value problem and its exact solution y(x) are given below. Apply Euler's meu
twice to approximate to this solution on the interval [0, ½], first with step size h = 0 25
(two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place
values of the two approximations at x = 2 with the value y(½) of the actual solution.
y' =(1+y?),y(0) = 1; y(x) :
= tan (x + T)
"ехact"
approx.
h f(xn, Yn)
Yn+1
Xn+1
f(xn Yn)
in
Yn
Yn+1
1
1
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F404f3a78-f730-4773-ad7b-fe6612b342a7%2Ff837734d-8bfd-45fc-acdb-34814c9b6d8a%2F5l5q5od_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. An initial value problem and its exact solution y(x) are given below. Apply Euler's meu
twice to approximate to this solution on the interval [0, ½], first with step size h = 0 25
(two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place
values of the two approximations at x = 2 with the value y(½) of the actual solution.
y' =(1+y?),y(0) = 1; y(x) :
= tan (x + T)
"ехact"
approx.
h f(xn, Yn)
Yn+1
Xn+1
f(xn Yn)
in
Yn
Yn+1
1
1
4
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