The industry demand for accurate and fast algorithms that model vital battery parameters, e.g., state-of-health, state-of-charge, pulse-power capability, is substantial. One of the most critical models is battery capacity fade. The key challenge with physics-based battery capacity fade modeling is the high numerical cost in solving complex models. In this study, an efficient and fast model is presented to capture capacity fade in lithium-ion batteries. Here, the high-order Chebyshev spectral method is employed to address the associated complexity with physics-based capacity fade models. Its many advantages, such as low computational memory, high accuracy, exponential convergence, and ease of implementation, allow us to efficiently model a comprehensive array of degradation physics such as solid electrolyte interface film formation, hydrogen evolution, manganese deposition, salt decomposition, manganese dissolution, and electrolyte oxidation. In this work, we developed a modeling framework that accurately and efficiently predicted degradation in a lithium-ion battery over extended cycles. For example, in long cycle battery operation, the implemented Chebyshev spectral method algorithm was found to be within 0.1358% - 0.28% of a high-fidelity model, while simulation times were reduced by an average of 91%. The developed Chebyshev spectral method algorithm shows great potential in advanced battery management systems, where maintaining accuracy and achieving a fast response is critical.