Solve the following problem with the fourth-order RK method: d?y dy +3 dx 2 + 3.125y = sin x dx2 where y(0) = 5 and y'(0) = 3. Solve from x = 0 to 5 with h = 0.5. %3D Find the error considering the exact solution is y(x) = e -0.75x *(5.292237 cos x+6.859589 sin x)-0.292237 cos x+0.109589 sin x Display the analytical and numerical results on the same graph.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Use six decimal digits with rounding in calculations.

Solve the following problem with the fourth-order RK method:
d²y
dy
2
+ 3
+ 3.125y = sin x
dx?
dx
where y(0) = 5 and y'(0) = 3. Solve from x = 0 to 5 with h = 0.5.
Find the error considering the exact solution is
y(x) = e
075* (5.292237 cos x+ 6.859589 sin x)-0.292237 cos x+0.109589 sin x
%3D
Display the analytical and numerical results on the same graph.
Transcribed Image Text:Solve the following problem with the fourth-order RK method: d²y dy 2 + 3 + 3.125y = sin x dx? dx where y(0) = 5 and y'(0) = 3. Solve from x = 0 to 5 with h = 0.5. Find the error considering the exact solution is y(x) = e 075* (5.292237 cos x+ 6.859589 sin x)-0.292237 cos x+0.109589 sin x %3D Display the analytical and numerical results on the same graph.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 1 images

Blurred answer
Knowledge Booster
Exponents
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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,