 An implicit-explicit Runge-Kutta-Chebyshev finite element method for the nonlinear Lithium-ion battery equationsR. Bermejo and P. Galán del Sastre Applied Mathematics and Computation, 2019, vol. 361, issue C, 398-420 Abstract: We introduce a numerical method to integrate the nonlinear system of equations that model the physical-chemical laws of the Lithium-ion batteries. The mathematical model, formulated in Doyle et al. J. Electrochem. Soc. 140 (1993) 1526–1533, is a system of strongly coupled nonlinear parabolic and elliptic equations. Our numerical method combines a second order implicit–explicit Runge–Kutta–Chebyshev scheme for time discretization of the parabolic equations governing the dynamics of the variables ce and cs, with linear finite element space discretization of the system. The implicit-explicit numerical formulation of the parabolic equations allows us to decouple the strong nonlinear reaction terms, which are treated implicitly, from the linear diffusion terms, treated explicitly. This approach is computationally efficient because (a) it has an extended stability region, and (b) the coupled system of algebraic equations becomes a single variable nonlinear equation per mesh point, which is easily solved by Newton method. Keywords: Lithium-ion battery; Implicit–explicit Runge–Kutta–Chebyshev scheme; Finite element method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:398-420 DOI: 10.1016/j.amc.2019.05.011 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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