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i want you to solve this problem and i will send for you file PDF with my lecture
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Work Independently
1 Solve
Urz(x, y)+ Uyy(x, y) = 0, 0 < x
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Explanation & Answer
Hi, Please check the attached file for details, let me know if you have any questions, thank you. James,
1. First homogenize the boundary equation on x, let U(x,y) = w(x,y) + d1 +x/a(d2-d1), since
d1 +x/a(d2-d1) = d1 at x=0 and d1 +x/a(d2-d1) = d2 at x=a, the boundary conditions for w(x,y)
becomes
w(0,y) =w(a,y)=0
w(x,0) = u(x,0) – d1 = f(x)-d1
w(x,b) = u(x,b)-d2 = 0-d2 = -d2
Using method of separation of variables to solve w(x,y), let
w( x, y ) X ( x)Y ( y )
plugging it into the equation we have
X ' ' ( x)Y ( y ) X ( x)Y ' ' ( y ) ...
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