Question 1 The heat equation is defined as, ди ,0 < x < 5,t > 0 with the boundary conditions u (0, t) = 1, u (5, t) = 4, t > 0 %3D and initial condition u (x, 0) = x²,0 < x < 5. 1. For Ax = 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

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Numerical method
Question 1
The heat equation is defined as,
ди
= 2
Əx?
0 < x < 5, t > 0
with the boundary conditions
и (0, t) — 1, и (5, t) — 4, t > 0
and initial condition
u (x, 0) = x²,0 < x < 5.
1. For Ax = 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.
Transcribed Image Text:Question 1 The heat equation is defined as, ди = 2 Əx? 0 < x < 5, t > 0 with the boundary conditions и (0, t) — 1, и (5, t) — 4, t > 0 and initial condition u (x, 0) = x²,0 < x < 5. 1. For Ax = 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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