Solve the boundary value problem. U₁ = Uzz u(-1, t) = u(1, t) and u₂(-1, t) = u₂(1, t) u(x, 0) = 2x4 - 4x² +1 u(x, t) = + B=1 if -1 0 if t > 0 if -1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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You are expected to do some subsequent simplification for your final answer.
Solve the boundary value problem.
Ut = UII
u( − 1, t) = u(1, t) and u₁( − 1, t) = u₂(1, t)
u(x, 0) = 2x¹ - 4x² + 1
u(x, t) =
=
+
n=1
if −1<x< 1 and t > 0
if t > 0
if
−1≤x≤1
Transcribed Image Text:You are expected to do some subsequent simplification for your final answer. Solve the boundary value problem. Ut = UII u( − 1, t) = u(1, t) and u₁( − 1, t) = u₂(1, t) u(x, 0) = 2x¹ - 4x² + 1 u(x, t) = = + n=1 if −1<x< 1 and t > 0 if t > 0 if −1≤x≤1
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