Lecture
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.