Diffusion on a One-dimensional Lattice with an Absorbing Boundary. Consider a one-dimensional lattice consisting of
Assume that the left endpoint is a reflecting boundary so that the rate equation for the number of particles
(a) Find the system of differential equations that describe the rate equation for
(b) Site
and explain the meaning of this equation.
(c) Find the eigenvalues and eigenvectors for the matrix
(d) Find the general solution of the system of equations found in part (a).Explain the asymptotic behavior of
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Differential Equations: An Introduction to Modern Methods and Applications
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