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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 34RE
Question
![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) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d9e45e4-143b-4ce2-96d2-a0cd33451ff1%2F35f6cd8e-a7d3-47fe-a1b1-72bcb3be32c7%2Firlp7lk_processed.png&w=3840&q=75)
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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