Question 1 The heat equation is defined as, du ,0 < x < 5,t > 0 at with the boundary conditions u (0, t) = 1, u (5, t) = 4, t > 0 and initial condition u (x,0) = a²,0 < x < 5. 1. For Ar = h = 1 and At = k = 0.1, sketch a suitable diagram to show the grid points where the solution are calculated and label all the initial solution until t = 0.1. 2. Use Crank-Nicolson method to find the solution for 0
Question 1 The heat equation is defined as, du ,0 < x < 5,t > 0 at with the boundary conditions u (0, t) = 1, u (5, t) = 4, t > 0 and initial condition u (x,0) = a²,0 < x < 5. 1. For Ar = h = 1 and At = k = 0.1, sketch a suitable diagram to show the grid points where the solution are calculated and label all the initial solution until t = 0.1. 2. Use Crank-Nicolson method to find the solution for 0
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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do Q1 2 ONLY
Transcribed Image Text:Question 1
The heat equation is defined as,
u
du
= 2-
,0 < x < 5,t > 0
at
with the boundary conditions
u (0, t) = 1, u (5, t) = 4, t > 0
and initial condition
u (x, 0) = x2,0 <x < 5.
1. For Ar = h = 1 and At = k = 0.1, sketch a suitable diagram to show the grid
points where the solution are calculated and label all the initial solution until
t = 0.1.
2. Use Crank-Nicolson method to find the solution for 0 <t <0.1 and solve the linear
system Au = b using Thomas Algorithm.
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