Existence and uniqueness of solutions to discrete diffusion equations

Motivated by the classical one-dimensional diffusion equation, utkuxx = f(x,t), x∊R, t≥0,u(x,0)=∊(x), x∊R, we find the unique solution of the partial difference equation δtu(x,t)-kδ2x,xu(x-1,t)=f(x,t), x∊Z, t≥0,u(x,0)=∊(x), x∊Z, where <F>k ∊ (0, 1)</F>. Our approach is to construct the Green''s function for the appropriate partial difference operator, and almost immediately we establish an existence and uniqueness result for the discrete nonhomogenous problem. [Copyright &y& Elsevier]