Problem 14.1.13: Find the steady-state temperature u(r, 0) in a quarter- circular plate. The boundary value problem is д^и 1 ди 1 д?и dr² ™ r ər ™ r2 a0² : = 0, 0<0<;. 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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Problem 14.1.13: Find the steady-state temperature u(r,0) in a quarter-
circular plate. The boundary value problem is
1 a²u
a²u 1ðu
+-
ar2
π
r ər ' r² a02
- z•
= 0, 0<0 <•
0 <r<c
u(c, 8) = f(8), 0 < 0 <÷
2
u(r,0) = 0, u(r,) = 0,
0 <r<c
Transcribed Image Text:Problem 14.1.13: Find the steady-state temperature u(r,0) in a quarter- circular plate. The boundary value problem is 1 a²u a²u 1ðu +- ar2 π r ər ' r² a02 - z• = 0, 0<0 <• 0 <r<c u(c, 8) = f(8), 0 < 0 <÷ 2 u(r,0) = 0, u(r,) = 0, 0 <r<c
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