Comparative Performance Analysis of Numerical Discretization Methods for Electrochemical Models of Lithium-ion Batteries

Abstract

This study evaluates numerical discretization methods for the Single Particle Model (SPM) used in electrochemical modeling. The methods include the Finite Difference Method (FDM), spectral methods, Pad\'e approximation, and parabolic approximation. Evaluation criteria are accuracy, execution time, and memory usage, aiming to guide method selection for electrochemical models. Under constant current conditions, the FDM explicit Euler and Runge-Kutta methods show significant errors, while the FDM implicit Euler method improves accuracy with more nodes. The spectral method achieves the best accuracy and convergence with as few as five nodes. The Pad\'e approximation exhibits increasing errors with higher current, and the parabolic approximation shows higher errors than the converged spectral and FDM implicit Euler methods. Under dynamic conditions, frequency domain analysis indicates that the FDM, spectral, and Pad\'e approximation methods improve high-frequency response by increasing node count or method order. In terms of execution time, the parabolic method is fastest, followed by the Pad\'e approximation. The spectral method is faster than FDM, while the FDM implicit Euler method is the slowest. Memory usage is lowest for the parabolic and Pad\'e methods, moderate for FDM, and highest for the spectral method. These findings provide practical guidance for selecting discretization methods under different operating scenarios.