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Given the heat equation, U₁=Uxx, 00 XX u(0,t)= u(2,t)=0, t≥0 u(x,0)=3x(2-x),

Given the heat equation, U₁=Uxx, 00 XX u(0,t)= u(2,t)=0, t≥0 u(x,0)=3x(2-x),

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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EXERCISES 3.8 Based on the information in Example 3.44 with the same step size At-0.01 and 5-04, solve the given 1D heat problem up to t-0.02. 2 Given the heat equation, Answer: 1. U₁ = Uxx + u(0,t)= u(1,t)=0, u(x,0)=x(1-x), with the steps size At=0.01 and Ax=0.2. Determine all the values of the end points and interior points of the first row of the problem. 40,2 = 0 1,2 = 1.80 42,2 = 2.7075 U3,2 = 2.7563 4,2 = 1.8038 0<x<1, 45,2 = 0. t>0, 120, 2. End points Chapter 3 : Interior points: 0,0 = 0 and u5,0 =0. ₁0=0.16, ₂0=0.24, U3,0 = 0.24, U4,0 = 0.16.
Transcribed Image Text:EXERCISES 3.8 Based on the information in Example 3.44 with the same step size At-0.01 and 5-04, solve the given 1D heat problem up to t-0.02. 2 Given the heat equation, Answer: 1. U₁ = Uxx + u(0,t)= u(1,t)=0, u(x,0)=x(1-x), with the steps size At=0.01 and Ax=0.2. Determine all the values of the end points and interior points of the first row of the problem. 40,2 = 0 1,2 = 1.80 42,2 = 2.7075 U3,2 = 2.7563 4,2 = 1.8038 0<x<1, 45,2 = 0. t>0, 120, 2. End points Chapter 3 : Interior points: 0,0 = 0 and u5,0 =0. ₁0=0.16, ₂0=0.24, U3,0 = 0.24, U4,0 = 0.16.
Example 3.44 Given the heat equation, U₁=Uxx, 0<x<2, t>0 u(0,t)= u(2,t)=0, t≥0 u(x,0)=3x(2-x). Cha
Transcribed Image Text:Example 3.44 Given the heat equation, U₁=Uxx, 0<x<2, t>0 u(0,t)= u(2,t)=0, t≥0 u(x,0)=3x(2-x). Cha
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