Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method twice to approximate to this solution on the interval [O, 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 = with the value y(%) of the actual solution. y' = (1 + y²),y(0) = 1; y(x) = tan (x+1) approx. "exact" Xn f(xn Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 1 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 0.3 0.1 0.4 1.223049 0.4 0.1 0.5 1.287427 3. 4-

4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method twice to approximate to this solution on the interval [O, 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 = with the value y(%) of the actual solution. y' = (1 + y²),y(0) = 1; y(x) = tan (x+1) approx. "exact" Xn f(xn Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 1 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 0.3 0.1 0.4 1.223049 0.4 0.1 0.5 1.287427 3. 4-

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method 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 = h with the value y(%) of the actual solution. y' = (1 + y?), y(0) = 1; y(x) = tan (x +1) %3D approx. "ехact" Xn f(xn, Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 0 0 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 3 0.3 0.1 0.4 1.223049 4 0.4 0.1 0.5 1.287427
Transcribed Image Text:4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method 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 = h with the value y(%) of the actual solution. y' = (1 + y?), y(0) = 1; y(x) = tan (x +1) %3D approx. "ехact" Xn f(xn, Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 0 0 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 3 0.3 0.1 0.4 1.223049 4 0.4 0.1 0.5 1.287427
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS