Consider the boundary value problem d2phi / dx2 + lambda phi = 0, with phi(0) -
ID: 1852239 • Letter: C
Question
Consider the boundary value problem d2phi / dx2 + lambda phi = 0, with phi(0) - d phi / dx (0) = 0 and phi(1) + d phi / dx(1) = 0. Using Rayleigh quotient show that lambda > 0. Prove that Eigenfunctions corresponding to different eigenvalues are orthogonal. Show that equation tan root lambda = 2 root lambda/(lambda - 1) can be used to determine the eigenvalues. Based on the graphical technique, estimate the largest two eigenvalues. Suppose u(x, 0) = f(x), u(0, t) - u / x (0, t) = 0 and u(1, t) + u / x (1,t) = 0, assuming the relevant Eigenfunctions are known, solve u / t = k 2 u / x2.Explanation / Answer
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