5.) Find the explicit finite difference solution of the wave equationUtt – Urr = 0,0 < x < 1, t> 0,with the boundary conditionsu (0, t) = u (1, t) = 0,t> 0,and the initial conditionsu (x, 0) = sin 7x,Ut (x, 0) = 0,0 < x < 1.Compare the numerical solution with the analytical solution u (x, t) = coS At sin ax at pointsU1, 1, U2, 1, and u1,2. Use Ax = At = 0.1.

Given: The wave equation, utt-uxx=0 , 0<x<1, t>0 with boundary conditions,…

5.) Find the explicit finite difference solution of the wave equation Utt - Uzz = 0, 0 0, with the boundary conditions u (0, t) = u (1, t) = 0, t> 0, and the initial conditions u (x, 0) = sin 7æ, ut (x, 0) = 0, 0

5.) Find the explicit finite difference solution of the wave equation Utt - Uzz = 0, 0 0, with the boundary conditions u (0, t) = u (1, t) = 0, t> 0, and the initial conditions u (x, 0) = sin 7æ, ut (x, 0) = 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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Question

5.) Find the explicit finite difference solution of the wave equation
Utt – Urr = 0,
0 < x < 1, t> 0,
with the boundary conditions
u (0, t) = u (1, t) = 0,
t> 0,
and the initial conditions
u (x, 0) = sin 7x,
Ut (x, 0) = 0,
0 < x < 1.
Compare the numerical solution with the analytical solution u (x, t) = coS At sin ax at points
U1, 1, U2, 1, and u1,2. Use Ax = At = 0.1.

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