4.17 Solve the wave equation u, + Uz = 0 on a digital computer using (a) Lax scheme (b) Lax-Wendroff scheme for the initial condition

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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solve the wave equation ut+ux=0 on a digital computer using Lax Scheme and Lax-Wendroff scheme

4.17 Solve the wave equation u, + u, - 0 on a digital computer using
(a) Lax scheme
(b) Lax-Wendroff scheme
for the initial condition
u(x,0) = sin 2nm|:
40
0 <x< 40
and periodic boundary conditions. Choose a 41 grid point mesh with Ax = 1 and compute to f = 18.
Solve this problem for n - 1, 3 and v = 1.0, 0.6, 0.3 and compare graphically with the exact solution.
Determine B for n = 1 and n = 3, and calculate the errors in amplitude and phase for each scheme
with v = 0.6. Compare these errors with the errors appearing on the graphs.
Transcribed Image Text:4.17 Solve the wave equation u, + u, - 0 on a digital computer using (a) Lax scheme (b) Lax-Wendroff scheme for the initial condition u(x,0) = sin 2nm|: 40 0 <x< 40 and periodic boundary conditions. Choose a 41 grid point mesh with Ax = 1 and compute to f = 18. Solve this problem for n - 1, 3 and v = 1.0, 0.6, 0.3 and compare graphically with the exact solution. Determine B for n = 1 and n = 3, and calculate the errors in amplitude and phase for each scheme with v = 0.6. Compare these errors with the errors appearing on the graphs.
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