Consider the Boundary Value problem a²u + = 0, 0 < x, y < 8 dy? и(х,0) — а(8 — г), и(п,8) — 0, 0<а<8 u(0, у) — 0, и(8, у) — 0, 0<у < 8 Using the separation of variables method, the solution u(x, y), is given by the series sinh (n (8 – u) (n-) 00 4 u(x, y) bn sin sinh(n 7) where bn =
Consider the Boundary Value problem a²u + = 0, 0 < x, y < 8 dy? и(х,0) — а(8 — г), и(п,8) — 0, 0<а<8 u(0, у) — 0, и(8, у) — 0, 0<у < 8 Using the separation of variables method, the solution u(x, y), is given by the series sinh (n (8 – u) (n-) 00 4 u(x, y) bn sin sinh(n 7) where bn =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 4CEXP
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Transcribed Image Text:Assignment06: Problem 15
Consider the Boundary Value problem
+
= 0, 0< a, y < 8
dy?
u(а, 0) — 2(8 — т), и(г,8) — 0, 0<т<8
u(0, у) — 0, и(8, у) — 0, 0<у< 8
Using the separation of variables method, the solution u(x, y), is given by the series
sinh (n(8 – u)
4
u(x, y)
bn sin (n
%3D
73
n=1
sinh(n n)
where
bn =
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