Consider the Laplace's equation u t uyy =0 in the square 00 find the associated eigenfunctions X,(x) for n = 1,2,3, c) Using the boundary condition calculate Y, ) d) Calculate the coefficients (c,) to satisfy the nonhomogeneous condition e) Write a formal series solution of the problem.
Consider the Laplace's equation u t uyy =0 in the square 00 find the associated eigenfunctions X,(x) for n = 1,2,3, c) Using the boundary condition calculate Y, ) d) Calculate the coefficients (c,) to satisfy the nonhomogeneous condition e) Write a formal series solution of the problem.
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Transcribed Image Text:Consider the Laplace's equation u t uyy = 0 in the square 0<x<R, 0<y<n and given
boundary values conditions u(0, y) = u(n, y) u(x,0) 0, u(x, ") = f(x) = 50.
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u = f(x)
R
u=0
u=0
u= 0
a) Calculate the eigenvalue 2. Consider all possible (real) values of A. Show explicitly that à= 0
and A <0 are not eigenvalues of the problem,
b) For A, >0 find the associated eigenfunctions X,(x) forn= 1,2,3, -
c) Using the boundary condition calculate Y, y)
d) Calculate the coefficients (c,) to satisfy the nonhomogeneous condition
e) Write a formal series solution of the problem.
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