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<p>This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for approximating second-order semi-linear initial value problems. The method is exploited using the scaling and restoring technique based on a quadruple angle formula in conjunction with a truncated Taylor series. The choice of the scaling parameter and the degree of the Taylor polynomial relies on a forward error analysis. Numerical experiments show that the new algorithm behaves in a stable fashion and performs well in both accuracy and efficiency.</p>

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Efficient algorithm for the oscillatory matrix functions

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Dongping Li,
  • Xue Wang,
  • Xiuying Zhang

摘要

This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for approximating second-order semi-linear initial value problems. The method is exploited using the scaling and restoring technique based on a quadruple angle formula in conjunction with a truncated Taylor series. The choice of the scaling parameter and the degree of the Taylor polynomial relies on a forward error analysis. Numerical experiments show that the new algorithm behaves in a stable fashion and performs well in both accuracy and efficiency.