Pseudo-two-dimensional (P2D) model is a detailed electrochemical model, which is widely used in the field of Li-ion batteries and proves to be an accurate model when suitably calibrated. However, due to its computational burden for applications such as control, state estimation, and cell characterization various reduced order models are developed. In this work, a simulation tool is proposed considering a modified single particle model including electrolyte dynamics (SPMe) which provides higher prediction accuracy compared to a single particle model, especially at high C-rates. In the proposed approach, all the governing partial differential equations are solved analytically without further simplification. Therefore, the computational burden is significantly reduced compared to an equivalent numerical solution, since the need for spatial discretization and time stepping is eliminated when the time-varying boundary condition is known.