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4. Given the initial value problem for the heat equation as follows: ôu_ d²u 00 и (0,г) - и (2,1)-0, 120 u(x,0) = sin 27x Use finite difference formula to find the value of u(x,t), for t = 0.2 if At = 0.1 and 4x = 0.4. (i) Answer: (i) U0.0 = u(0,0) = 0;4,0 = 0.5878;u20 =-0.9511;u30 = 0.9511;40 =-0.5878;u50 =0 U01 = 0; 41 =-0.7414;u21 = 1.1996; 131 = -1.1996; 41 = 0.7414;u51 = 0 19,2 = 0; 412 = 0.9351;u,, =-1.5130;U32 = 1.5130;u42 = -0.9351;152 = 0 %3D %3D

4. Given the initial value problem for the heat equation as follows: ôu_ d²u 00 и (0,г) - и (2,1)-0, 120 u(x,0) = sin 27x Use finite difference formula to find the value of u(x,t), for t = 0.2 if At = 0.1 and 4x = 0.4. (i) Answer: (i) U0.0 = u(0,0) = 0;4,0 = 0.5878;u20 =-0.9511;u30 = 0.9511;40 =-0.5878;u50 =0 U01 = 0; 41 =-0.7414;u21 = 1.1996; 131 = -1.1996; 41 = 0.7414;u51 = 0 19,2 = 0; 412 = 0.9351;u,, =-1.5130;U32 = 1.5130;u42 = -0.9351;152 = 0 %3D %3D

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. Given the initial value problem for the heat equation as follows: ди ди 0<x< 2, t>0 %3D ốt u(0,t)=u(2,1)= 0, t20 u(x,0) = sin 27x (i) Use finite difference formula to find the value of u(x,t), for t = 0.2 if At = 0.1 and Ax = 0.4. Answer: (i) U0.0 = u(0,0) = 0:40 = 0.5878;u20 =-0.9511:u30 = 0.9511:440 = -0.5878;u50 = 0 Uo1 = 0; 41 =-0.7414;u1 = 1.1996; u31 =-1.1996;u41 = 0.7414;u51 = 0 U0,2 = 0;442 = 0.9351;u,2 = -1.5130; 132 = 1.5130;442 = -0.9351:u52 = 0
Transcribed Image Text:4. Given the initial value problem for the heat equation as follows: ди ди 0<x< 2, t>0 %3D ốt u(0,t)=u(2,1)= 0, t20 u(x,0) = sin 27x (i) Use finite difference formula to find the value of u(x,t), for t = 0.2 if At = 0.1 and Ax = 0.4. Answer: (i) U0.0 = u(0,0) = 0:40 = 0.5878;u20 =-0.9511:u30 = 0.9511:440 = -0.5878;u50 = 0 Uo1 = 0; 41 =-0.7414;u1 = 1.1996; u31 =-1.1996;u41 = 0.7414;u51 = 0 U0,2 = 0;442 = 0.9351;u,2 = -1.5130; 132 = 1.5130;442 = -0.9351:u52 = 0
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