The neutron diffusion equation with a (plane) source at x = 0 is d² f(x) dx² · + w² f(x) = Q(x) where f(x) is the flux of neutrons (|f(x) → 0 as x → ∞), Q8(x) is the plane source at x = 0 (where (x) is the Dirac delta function), and w² is a constant. (a) Fourier transform this equation for f(x) and write the corresponding equation that is satisfied by F(k), the transform of f(x). (b) Solve the equation you found in part (a) for F(k). (c) Find f(x) by using the inverse Fourier transform to obtain the solution for all x = (-∞, ∞).
The neutron diffusion equation with a (plane) source at x = 0 is d² f(x) dx² · + w² f(x) = Q(x) where f(x) is the flux of neutrons (|f(x) → 0 as x → ∞), Q8(x) is the plane source at x = 0 (where (x) is the Dirac delta function), and w² is a constant. (a) Fourier transform this equation for f(x) and write the corresponding equation that is satisfied by F(k), the transform of f(x). (b) Solve the equation you found in part (a) for F(k). (c) Find f(x) by using the inverse Fourier transform to obtain the solution for all x = (-∞, ∞).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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