MATLAB ODE Solvers Benchmarked: The Hidden Trade-offs Between Accuracy, Stability, and Speed

Selecting the right ODE solver is not just about minimizing computational error—it's a critical decision that impacts stability, energy conservation, and long-term solution quality across diverse physical systems. This study reveals that solvers excelling in one domain (stiff chemical kinetics, oscillatory systems, chaos) may catastrophically fail in others, and that computational efficiency often involves careful trade-offs with accuracy and physical correctness. For MATLAB users in control engineering, robotics, and computational physics, this benchmark framework provides essential guidance for matching solver selection to problem characteristics.