At Use Lax-Wendroff method_(λ = a Ax to approximate Ui,j+1 1 = - (U₁+1, + U₁-1,1) - (U+1.) - Ui-1,1) Ut - 5ux = 0, 0≤x≤2,t> 0 u(x,0) = sin IX. For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution u(x, t) = = sin π(x + 5t) at t = 0.4. which one gives you stable solutions? (a) Ax = 0.5 and At = 0.2 (b) Ax = 0.5 and At = 0.1
At Use Lax-Wendroff method_(λ = a Ax to approximate Ui,j+1 1 = - (U₁+1, + U₁-1,1) - (U+1.) - Ui-1,1) Ut - 5ux = 0, 0≤x≤2,t> 0 u(x,0) = sin IX. For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution u(x, t) = = sin π(x + 5t) at t = 0.4. which one gives you stable solutions? (a) Ax = 0.5 and At = 0.2 (b) Ax = 0.5 and At = 0.1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![4. Use Lax-Wendroff method_(λ = a a At
Ax
to approximate
1
Ui.j+1 = ½ (U+1.) + Ui-1,j) — 2/2 (U+1.) — U₁-1,))
2
-
ut 5ux = 0, 0≤x≤ 2,t> 0
-
u(x, 0)
= = sin лx.
For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution
u(x, t) = sin π(x + 5t) at t = 0.4. which one gives you stable solutions?
(a) Δx
= 0.5 and At
0.2
(b) Ax = 0.5 and At = 0.1
(You may just write down the U values at each mesh point on the graph below.)
t
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd83c3ce1-cd72-4e3b-8702-f62923bac270%2Fa5953260-a5e5-4381-8336-93e318760f18%2Fgeqlcv5_processed.png&w=3840&q=75)
Transcribed Image Text:4. Use Lax-Wendroff method_(λ = a a At
Ax
to approximate
1
Ui.j+1 = ½ (U+1.) + Ui-1,j) — 2/2 (U+1.) — U₁-1,))
2
-
ut 5ux = 0, 0≤x≤ 2,t> 0
-
u(x, 0)
= = sin лx.
For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution
u(x, t) = sin π(x + 5t) at t = 0.4. which one gives you stable solutions?
(a) Δx
= 0.5 and At
0.2
(b) Ax = 0.5 and At = 0.1
(You may just write down the U values at each mesh point on the graph below.)
t
O
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