Model-based optimization and control are often employed to regulate batteries; however, such modeling tools are required to predict battery status fast and accurately. In this work, we present two modeling frameworks that help significantly decrease computational time while modeling battery physics accurately. These frameworks employ the Chebyshev spectral method for discretization of the governing equations, while integration of the resulting discretized system is implemented using either a segregated or a differential-algebraic equation formulation. The segregated formulation relies on linearized reaction rate kinetics, which enables easy coupling with the governing equations. Our choice of the Chebyshev spectral method is due to its exponential convergence and use of few discretization nodes, compared to conventional methods, such as finite difference method and finite element method. An average of about 98% reduction in computational time for the differential-algebraic equation framework was gained, while for the segregated algorithm, on average, a 51% reduction in computational time relative to the finite element method reference was realized. For all of these frameworks, the Chebyshev spectral method results were on the average within 0.07% - 0.39% of the high-fidelity finite element method reference.