u(x,t) is solution to steady state 2-D heat equation, d'u d'u -=0,with following parameters for numerical approximation: dx² dy ² + u= u(0,0), u (0,y)=0, u(1,y) = y(1-y), 0

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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d²u
d²u
u(x,t) is solution to steady state 2-D heat equation, +
dx² ду2
-=0,with following parameters for numerical approximation:
u = u(0,0), u(0,y)=0, u(1,y)=y(1-y), 0<y<2, u(x,0)=0, u(x,2) = x(1-x), 0<x<1, mesh size =0.5.
00
a. Write the approximate difference equation for this equation.
b. Calculate the point u (0.5, 1). (You don't need any computer programming here, you can calculate this by hand)
Transcribed Image Text:d²u d²u u(x,t) is solution to steady state 2-D heat equation, + dx² ду2 -=0,with following parameters for numerical approximation: u = u(0,0), u(0,y)=0, u(1,y)=y(1-y), 0<y<2, u(x,0)=0, u(x,2) = x(1-x), 0<x<1, mesh size =0.5. 00 a. Write the approximate difference equation for this equation. b. Calculate the point u (0.5, 1). (You don't need any computer programming here, you can calculate this by hand)
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