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Extrapolation of Implicit Runge-Kutta Methods in Solving Simple Harmonic Oscillators and Simple Pendulum Problems

Annie Gorgey


The research is to show the effect of passive and active extrapolation in solving simple harmonic oscillators (SHO), simple pendulum (SP) and Kepler problems. The efficiency
between the two modes of extrapolation; passive and active are compared. The studies are done theoretically and numerically on the simple harmonic oscillator problem. Theoretically, it showed that both active and passive extrapolation give linear error growth for a reasonable stepsize and on a small interval. Quadratic error growth is observed on both modes of extrapolation for longer intervals. The numerical experiments for SHO problem showed that passive extrapolation is advantageous than active extrapolation. The behaviour of passive extrapolation is also observed to give more stable solutions over long time interval for IMR and ITR. Hence, on all the problems, passive extrapolation is more efficient than active extrapolation.


symmetric, symplectic, extrapolation, simple harmonic oscillator, simple pendulum, linear error growth, quadratic error growth.

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