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In this work we introduce a new predictor–corrector (PC) pair form (SEPCM) for the numerical integration of second-order initial-value problems and a new optimized eight-step symmetric predictor–corrector method with minimal phase-lag and algebraic order ten is constructed. The new method is based on the multistep symmetric method of Quinlan–Tremaine (Astron. J. 100(5):1694–1700, 1990), with eight...
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