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In this paper, we propose the weak N-best pre-orthogonal adaptive Fourier decomposition (weak N-best POAFD) method for solving second-order initial value problems (IVPs). By introducing a novel weak N-best maximal selection principle, the method constructs orthogonal bases that maximize energy capture at each iterative step. Theoretical analysis demonstrates that the proposed approach achieves a higher convergence rate compared to standard POAFD. Numerical experiments confirm an order-of-magnitude improvement in accuracy.

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Weak N-Best POAFD for Second Order Initial Value Problems of Ordinary Differential Equation

  • 会议论文

  • 发表日期：

    2026年

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  • Hongfang Bai,
  • Jianwei Dong

摘要

In this paper, we propose the weak N-best pre-orthogonal adaptive Fourier decomposition (weak N-best POAFD) method for solving second-order initial value problems (IVPs). By introducing a novel weak N-best maximal selection principle, the method constructs orthogonal bases that maximize energy capture at each iterative step. Theoretical analysis demonstrates that the proposed approach achieves a higher convergence rate compared to standard POAFD. Numerical experiments confirm an order-of-magnitude improvement in accuracy.