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...

See similar textbooks