Short- and long-time solutions for material balance equation in lithium-ion batteries by Laplace transform

Short- and long-time solutions for material balance equations for porous electrodes in both the solid and the solution phase is presented. These solutions represent the concentration profile of lithium-ions in the solid and solution phases of the positive electrode of a lithium-ion cell, and are obtained using the method of Laplace transform for short- and long-time intervals.