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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
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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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
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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