Solve the following Laplace equation on a domain exterior to a circle: (r>a, π <0 < π) 1 Au = Urr +-Ur + T u, (a, 0) = 0, z100 =0 1 72 lim u(r, 0)- 3r cos 0 = 0. 818 (Hint: Note that this problem does not satisfy u(r, 0) < ∞ as r→∞. To solve this problem, try to write u(r, 0) 3r cos 0+v(r, 0) and solve the corresponding problem for v(r, 0).)
Solve the following Laplace equation on a domain exterior to a circle: (r>a, π <0 < π) 1 Au = Urr +-Ur + T u, (a, 0) = 0, z100 =0 1 72 lim u(r, 0)- 3r cos 0 = 0. 818 (Hint: Note that this problem does not satisfy u(r, 0) < ∞ as r→∞. To solve this problem, try to write u(r, 0) 3r cos 0+v(r, 0) and solve the corresponding problem for v(r, 0).)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please help me.
Thankyou.
Transcribed Image Text:1. Solve the following Laplace equation on a domain exterior to a circle:
1
Au = U₂² +2+
1
7-2
(r>a, -*<O<x)
u,(a,0) = 0, lim u(r, 0) 3r cos 0 = 0.
Uso = 0
(Hint: Note that this problem does not satisfy u(r, 0) < ∞ as r→ ∞. To solve this
problem, try to write u(r,0) = 3r cos 0 — v(r. 9) and solve the corresponding problem
for v(r.0).)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
