Given a wave equation: 7.5 ,00 Subject to boundary conditions: u(0,t) = 0, u(2,t) = 1 for 0 ≤ t ≤ 0.4 An initial conditions: u(x,0)=2x Ju(x,0) at = 1 for 0≤x≤ 2 By using the explicit finite-difference method, analyse the wave equation by taking: h = Ax=0.5, k = At = 0.2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1
(b) Given a wave equation:
a²u
8²u
at²
0x2x
= 7.55
,0<x<2, t>0
Subject to boundary conditions:
u(0,t) = 0, u(2, t) = 1 for 0 ≤ t ≤ 0.4
An initial conditions:
u(x,0) = ² 2x au(x,0)
at
= 1 for 0 ≤ x ≤ 2
By using the explicit finite-difference method, analyse the wave equation by taking:
h = Ax = 0.5, k = At = 0.2
Transcribed Image Text:(b) Given a wave equation: a²u 8²u at² 0x2x = 7.55 ,0<x<2, t>0 Subject to boundary conditions: u(0,t) = 0, u(2, t) = 1 for 0 ≤ t ≤ 0.4 An initial conditions: u(x,0) = ² 2x au(x,0) at = 1 for 0 ≤ x ≤ 2 By using the explicit finite-difference method, analyse the wave equation by taking: h = Ax = 0.5, k = At = 0.2
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