This paper presents comprehensive studies on frequency response optimized integrators considering second order derivative regarding their numerical error, numerical stability and transient performance. Frequency domain error analysis is conducted on these numerical integrators to reveal their accuracy. Numerical stability of the numerical integrators is investigated. Interesting new types of numerical stability are recognized. Transient performance of the numerical integrators is defined to qualitatively characterize their ability to track fast decaying transients. This property is related to unsatisfactory phenomena such as numerical oscillation which frequently appear in time domain simulation of circuits and systems. Transient performance analysis of the numerical integrators is provided. Theoretical observations from the analysis of the numerical integrators are verified via time domain case studies.
翻译：本文件介绍了关于最佳频率反应最佳集成器的全面研究,这些集成器考虑到数字误差、数字稳定性和瞬时性能的二阶衍生物;对这些数字集成器进行频率域错误分析,以显示其准确性;调查数字集成器的数值稳定性;认识到新的有趣的数字稳定性类型;数字集成器的短暂性能被界定为其跟踪快速衰变瞬时性的能力的质量特征;这一属性与不令人满意的现象有关,例如经常出现在时间域电路和系统模拟中的数值振荡现象;提供了数字集成器的中性性性性能分析;通过时间域案例研究核实了数字集成器分析得出的理论意见。
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