Solve Laplace's equation inside a rectangle 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
100%
I need help with my Laplace's equations inside a rectangle. Part of my assignment is letters b., d., f., g., and h. I am so confused.
![EXERCISES 2.5
2.5.1. Solve Laplace's equation inside a rectangle 0 < x < L, 0 < y < H, with the fol-
lowing boundary conditions [Hint: Separate variables. If there are two homogeneous
boundary conditions in y, let u(r, y) = h(x)o(y), and if there are two homogeneous
boundary conditions in z, let u(x, y) = 0(x)h(y).]:
*(a) (0, y) = 0,
(L, y) = 0, u(x,0) = 0,
u(r, H) = f(x)
(b) (0, y) = g(y),
(L,y) = 0, u(x,0) = 0,
u(x, H) = 0
*(c) (0, y) = 0,
au
u(L, y) = 9(y), u(x,0) = 0,
u(x, H) = 0
(d) u(0, y) = g(y), u(L, y) = 0,
(r, 0) = 0,
u(x, H) = 0
*(e) u(0, y) = 0,
u(L, y) = 0,
u(x,0) – (r, 0) = 0, u(r, H) = f(x)
du
(f) u(0, y) = f(y), u(L, y) = 0,
(z,0) = 0,
(z, H) = 0
(g) (0, y) = 0,
S0 a > L/2
11 r < L/2
au
au
(L,y) = 0, u(x, 0) =
(r, H) = 0
(h) u(0, y) = 0,
u(L, y) = g(y), u(x,0) = 0,
u(x, H) = 0
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028e02df-ce89-464d-926f-4d831e653f09%2F16a9b5ac-fa27-4f60-a3d9-f5507237042f%2Flat453q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISES 2.5
2.5.1. Solve Laplace's equation inside a rectangle 0 < x < L, 0 < y < H, with the fol-
lowing boundary conditions [Hint: Separate variables. If there are two homogeneous
boundary conditions in y, let u(r, y) = h(x)o(y), and if there are two homogeneous
boundary conditions in z, let u(x, y) = 0(x)h(y).]:
*(a) (0, y) = 0,
(L, y) = 0, u(x,0) = 0,
u(r, H) = f(x)
(b) (0, y) = g(y),
(L,y) = 0, u(x,0) = 0,
u(x, H) = 0
*(c) (0, y) = 0,
au
u(L, y) = 9(y), u(x,0) = 0,
u(x, H) = 0
(d) u(0, y) = g(y), u(L, y) = 0,
(r, 0) = 0,
u(x, H) = 0
*(e) u(0, y) = 0,
u(L, y) = 0,
u(x,0) – (r, 0) = 0, u(r, H) = f(x)
du
(f) u(0, y) = f(y), u(L, y) = 0,
(z,0) = 0,
(z, H) = 0
(g) (0, y) = 0,
S0 a > L/2
11 r < L/2
au
au
(L,y) = 0, u(x, 0) =
(r, H) = 0
(h) u(0, y) = 0,
u(L, y) = g(y), u(x,0) = 0,
u(x, H) = 0
%3D
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps
Knowledge Booster
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 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,
