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Given an initial-boundary value problem for one dimensional heat equation as below, 00, «(0.1) - (r.t) - 0, 120. u(x,0) = 2e" - cos(x). x20. with Ar = 0.2r, Ar =0.1 up to 1=0.2. Then, find all solutions of the blue nodes as illustrated in the following figure, using the equation Mp =0.2533(u + Mues) +0.4934u, . Use 4 decimal places in your caleulations. 0.2 0.4r 0.6r -0.8r x M3.0 -0.6127, m -0.1932, MA -0.6343, My=0.3767

Given an initial-boundary value problem for one dimensional heat equation as below, 00, «(0.1) - (r.t) - 0, 120. u(x,0) = 2e" - cos(x). x20. with Ar = 0.2r, Ar =0.1 up to 1=0.2. Then, find all solutions of the blue nodes as illustrated in the following figure, using the equation Mp =0.2533(u + Mues) +0.4934u, . Use 4 decimal places in your caleulations. 0.2 0.4r 0.6r -0.8r x M3.0 -0.6127, m -0.1932, MA -0.6343, My=0.3767

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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Question 5 Given an initial-boundary value problem for one dimensional heat equation as below, 0<x<R, t>0. u(0.1) = u(x.t) = 0, 120, u(x,0) = 2e" - cos (x). x20, with Ax = 0.2r, At =0.1 up to t= 0.2. Then, find all solutions of the blue nodes as illustrated in the following figure, using the equation 4, = 0.2533(4, + u)+0.4934u,. Use 4 decimal places in your caleulations. X = 0.2 x = 0.4 x3 =0.6 * = 0,8 x = 3,0 =0.6127, uu -0.1932, M41 -0.6343, 2 = 0.3767 ANSWER U,0 = 0.2580,u2, = 0.2602, u,, = 0.9710,u, = 0.3489,uz1 = 0.6142 Us1 = 0, u0.2 = 0, u12 = 0.1837, uz2 = 0.5521, u42 = 0.4685 %3D
Transcribed Image Text:Question 5 Given an initial-boundary value problem for one dimensional heat equation as below, 0<x<R, t>0. u(0.1) = u(x.t) = 0, 120, u(x,0) = 2e" - cos (x). x20, with Ax = 0.2r, At =0.1 up to t= 0.2. Then, find all solutions of the blue nodes as illustrated in the following figure, using the equation 4, = 0.2533(4, + u)+0.4934u,. Use 4 decimal places in your caleulations. X = 0.2 x = 0.4 x3 =0.6 * = 0,8 x = 3,0 =0.6127, uu -0.1932, M41 -0.6343, 2 = 0.3767 ANSWER U,0 = 0.2580,u2, = 0.2602, u,, = 0.9710,u, = 0.3489,uz1 = 0.6142 Us1 = 0, u0.2 = 0, u12 = 0.1837, uz2 = 0.5521, u42 = 0.4685 %3D
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