Use the Maximum / Minimum Principle for Lapla can be at most one solution, u(x, y) of the boundary-value problem in part (a). (a) I et che a
Use the Maximum / Minimum Principle for Lapla can be at most one solution, u(x, y) of the boundary-value problem in part (a). (a) I et che a
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
Transcribed Image Text:4 Let a and b be two given positive real numbers and let R be the following open
rectangle:
R= {(x, y) = R²|0<x<a, 0 <y<b}
(a) Use the method of separation of variables to derive a series solution u(x, y) of
the following boundary-value problem for Laplace's equation :
Au(x, y) = 0,
(x, y) = R,
u(0, y) = 0, u(a, y) = 0,
0≤ y ≤ b,
u(x,0) = 0, u(x, b) = f(x),
0≤x≤ a,
where f is a given function.
(b) What assumption(s) do you need to make about the function f in order for your
solution to part (a) to be valid?
(c) State the Maximum / Minimum Principle for Laplace's equation.
(a) Use the Maximum/ Minimum Principle for Laplace's equation to show that there
can be at most one solution, u(x, y) of the boundary-value problem in part (a).
(a) Tot 11 he the solution of the boundary-value problem in part (a). Let c be a
la
·1/0
11 She the circle.
12%
2%
2%
2%
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 2 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,
