Use the finite difference method to solve the following hyperbolic (wave equation) PDE อิน 1 ata อิริน 16 x² = 0, 0
Use the finite difference method to solve the following hyperbolic (wave equation) PDE อิน 1 ata อิริน 16 x² = 0, 0
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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Transcribed Image Text:Use the finite difference method to solve the following hyperbolic (wave equation) PDE
อิน
1
ata
อิริน
16 x²
= 0,
0<x<0.5, 0<t;
u(x, 0) = sinx, 0 ≤x≤n: and
Ju(x,0)
8t
= sin 4πx, 0 ≤ x ≤0.5
u(0,t) = u(x,t) = 0, 0<t;
with m =4, N=4 and T = 0.5
sint sin 4x
Compare your results at t = 0.5 to the actual solution u(x,t) =
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