Approximate analytical solutions for a shrinking core model for the discharge of a lithium iron-phosphate electrode by the Adomian decomposition method

In this paper, we solve the mathematical model that describes the variation of lithium concentration in a lithium iron-phosphate (LiFePO4LiFePO4) particle during the process of lithium intercalation into the particle with shrinking core during the discharge process. The model is composed of a second-order linear partial differential equation satisfied by the distribution function of lithium concentration with an unknown moving boundary function and an ordinary partial differential equation satisfied by these two unknown functions. An approximate analytic solution for the partial differential equation with undetermined parameters is first given by the Adomian decomposition method (ADM) and then we require it to satisfy the moving boundary condition to determine these parameters in order to obtain the solution for the model. We need not transform the moving boundary into a fixed boundary as in prior research. Our new approach in solving the model shows that the ADM is an efficient method for solving moving boundary problems. Based on the algorithm provided by the ADM, we decompose the complex operation of solving the model into a sequence of sub-operations which are easily implemented by using the numerical and symbolic operations in MATLAB. By completing these sub-operations, we obtain an accurate expression of the approximate analytic solution for engineering simulations.