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Use a computer as a computational aid. Use the difference equation ujj+1 = λU₁+1₁j + (1 - 22)uj + λu;-1,j to approximate the solution of the boundary-value problem a²u 0 < x < 6,0 < t < 1 ах2 u(0, t) = 0, u(6, t) = 0, 0 ≤ t ≤1 J1, 0

Use a computer as a computational aid. Use the difference equation ujj+1 = λU₁+1₁j + (1 - 22)uj + λu;-1,j to approximate the solution of the boundary-value problem a²u 0 < x < 6,0 < t < 1 ах2 u(0, t) = 0, u(6, t) = 0, 0 ≤ t ≤1 J1, 0

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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Use a computer as a computational aid. Use the difference equation U₁₁j+1 = λU¡+ 1,j + (1 − 2λ)u¡j + λu¡−1‚ƒ to approximate the solution of the boundary-value problem a²u ди ах2 at 0 < x < 6,0 < t < 1 u(0, t) = 0, u(6, t) = 0,0 ≤t≤1 1, 0<x<3 10, 3 < x≤ 6. = u(x, 0) = Use n = 8 and m = 40. (Give the approximations obtained for t = 1. Round your answers to four decimal places.) u(0.75, 1)~ u(1.50, 1) ~| u(2.25, 1)~ u(3.00, 1)~ u(3.75, 1)~| u(4.50, 1)~ u(5.25, 1)~ eBook
Transcribed Image Text:Use a computer as a computational aid. Use the difference equation U₁₁j+1 = λU¡+ 1,j + (1 − 2λ)u¡j + λu¡−1‚ƒ to approximate the solution of the boundary-value problem a²u ди ах2 at 0 < x < 6,0 < t < 1 u(0, t) = 0, u(6, t) = 0,0 ≤t≤1 1, 0<x<3 10, 3 < x≤ 6. = u(x, 0) = Use n = 8 and m = 40. (Give the approximations obtained for t = 1. Round your answers to four decimal places.) u(0.75, 1)~ u(1.50, 1) ~| u(2.25, 1)~ u(3.00, 1)~ u(3.75, 1)~| u(4.50, 1)~ u(5.25, 1)~ eBook
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