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Use a computer as a computational aid. Use the difference equation ujj+1 = Au¡+1,j + (1 − 2λ)u¡j + λu₁-1,j to approximate the solution of the boundary-value problem a²u au = əx² at " u(0, t) = 0, u(8, t) = 0, 0 ≤ts1 u(x, 0) = u(4.00, 1) = u(5.00, 1) = u(6.00, 1) = u(7.00, 1) = 0 < x < 8,0 < t < 1 1, 0, 0 < x≤ 4 4 < x≤ 8. Use n = 8 and m = 40. (Give the approximations obtained for t= 1. Round your answers to four decimal places.) u(1.00, 1) u(2.00, 1) = u(3.00, 1) =

Use a computer as a computational aid. Use the difference equation ujj+1 = Au¡+1,j + (1 − 2λ)u¡j + λu₁-1,j to approximate the solution of the boundary-value problem a²u au = əx² at " u(0, t) = 0, u(8, t) = 0, 0 ≤ts1 u(x, 0) = u(4.00, 1) = u(5.00, 1) = u(6.00, 1) = u(7.00, 1) = 0 < x < 8,0 < t < 1 1, 0, 0 < x≤ 4 4 < x≤ 8. Use n = 8 and m = 40. (Give the approximations obtained for t= 1. Round your answers to four decimal places.) u(1.00, 1) u(2.00, 1) = u(3.00, 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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Use a computer as a computational aid. Use the difference equation ujj+1 = Au¡+ 1,j + (1 − 2λ)u¡j + λu₁-1,j to approximate the solution of the boundary-value problem a²u au = əx² at 0 < x < 8,0 < t < 1 " u(0, t) = 0, u(8, t) = 0, 0 ≤ts1 u(x, 0) = u(4.00, 1) = u(5.00, 1) = u(6.00, 1) u(7.00, 1) = 1, 0, 0 < x≤ 4 4 < x≤ 8. Use n = 8 and m = 40. (Give the approximations obtained for t= 1. Round your answers to four decimal places.) u(1.00, 1) u(2.00, 1) = u(3.00, 1)
Transcribed Image Text:Use a computer as a computational aid. Use the difference equation ujj+1 = Au¡+ 1,j + (1 − 2λ)u¡j + λu₁-1,j to approximate the solution of the boundary-value problem a²u au = əx² at 0 < x < 8,0 < t < 1 " u(0, t) = 0, u(8, t) = 0, 0 ≤ts1 u(x, 0) = u(4.00, 1) = u(5.00, 1) = u(6.00, 1) u(7.00, 1) = 1, 0, 0 < x≤ 4 4 < x≤ 8. Use n = 8 and m = 40. (Give the approximations obtained for t= 1. Round your answers to four decimal places.) u(1.00, 1) u(2.00, 1) = u(3.00, 1)
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