Accuracy and Stability: Algorithms Performance

This lecture covers issues related to accuracy and stability in computational algorithms, focusing on the Verlet and Gear algorithms. The Verlet algorithm's stability is discussed in the context of a harmonic oscillator, highlighting the challenges of divergence and imaginary solutions. The Gear algorithm is introduced as a solution, emphasizing its predictor and corrector steps. Performance comparisons between various algorithms, including Euler, Verlet, and Gear, are presented through tests on a harmonic oscillator, evaluating accuracy, root-mean-square deviation, and energy drift.