# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Mon, 20 May 2013 21:49:56 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Laplaces equation help!!Posted: Thu, 15 Dec 2011 18:23:50 UTC
 S.O.S. Newbie

Joined: Thu, 15 Dec 2011 18:21:41 UTC
Posts: 1
1. Laplace equation's solution for (x,y) plane on a circle x>0, y>0 in polar coordinates with the conditions :
u(r=0,μ) = sinμ/sin∏/8 + sin μ/2 + cos μ/2 if 0≤μ≤π/2
u(r,μ=0) = √r if 0≤r≤1
u(r,μ=∏/2) = r^1/4 + √(2r) if 0≤r≤1

The equation is linear in u.
Use the variable separation method.

Sorry for my bad english, I hope it's understandable.

Top

 Post subject: Re: Laplaces equation help!!Posted: Thu, 15 Dec 2011 23:41:09 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6006
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
SandorVS wrote:
1. Laplace equation's solution for (x,y) plane on a circle x>0, y>0 in polar coordinates with the conditions :
u(r=0,μ) = sinμ/sin∏/8 + sin μ/2 + cos μ/2 if 0≤μ≤π/2
u(r,μ=0) = √r if 0≤r≤1
u(r,μ=∏/2) = r^1/4 + √(2r) if 0≤r≤1

The equation is linear in u.
Use the variable separation method.

Sorry for my bad english, I hope it's understandable.

Are you sure about the first condition? I suspect you want instead. Also, the last condition currently reads , the ^1 is redundant.

Recall the Laplacian in polar: . Separate variables you see , or a sum of these, are what you should try.

_________________

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous