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3. Use Lax-Friedrichs method (λ = a- to approximate O 1 λ - Vi,j+1 = 7 (Vi+1,j + Vi−1,j) − 2 (Ui+1,j — Ui−1,j) For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution u(x, t) = sin л(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 (You may just write down the U values at each mesh point on the graph below.) ta o ut 5ux = 0, 0≤x≤ 2,t> 0 u(x, 0) = sin лx. O- t O O

3. Use Lax-Friedrichs method (λ = a- to approximate O 1 λ - Vi,j+1 = 7 (Vi+1,j + Vi−1,j) − 2 (Ui+1,j — Ui−1,j) For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution u(x, t) = sin л(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 (You may just write down the U values at each mesh point on the graph below.) ta o ut 5ux = 0, 0≤x≤ 2,t> 0 u(x, 0) = sin лx. O- t O O

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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At. 3. Use Lax-Friedrichs method (λ = a · Ax to approximate λ Ui,j+1 = ½ (Ui+1,j + Ui−1,j) — ^ (Ui+1,j — Ui-1,j) ut 5ux = 0, 0≤x≤ 2,t> 0 u(x,0) = sin x. For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution u(x, t) = sin ï(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 (You may just write down the U values at each mesh point on the graph below.) t
Transcribed Image Text:At. 3. Use Lax-Friedrichs method (λ = a · Ax to approximate λ Ui,j+1 = ½ (Ui+1,j + Ui−1,j) — ^ (Ui+1,j — Ui-1,j) ut 5ux = 0, 0≤x≤ 2,t> 0 u(x,0) = sin x. For the following two sets of step sizes, compute solutions till t = 0.4. Then compare to the exact solution u(x, t) = sin ï(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 (You may just write down the U values at each mesh point on the graph below.) t
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