A mathematical model is presented for a lithium ion cell under galvanostatic discharge. The non-homogeneous material balance equation for the solution phase of a lithium cell was solved analytically using Green's function. We determined the elementary Solutions, the norms and the eigen values of the problems for galvanostatic boundary conditions and systematically tabulate the resulting expressions. The solution has been obtained in a closed form expression. (c) 2007 Elsevier B.V. All rights reserved.