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The classical fourth-order Runge-Katla integrator and the third-order force gradient symplectic integrator are used to solve the two-dimensional H'enon-Heiles system respectively. Numerical results, including the relative energy error, Poincare section, the largest Lyapunov exponent and Fast Lyapunov Indicator, are compared in detail. It is found that the Runge-Katla algorithm does not conserve the...
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