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<p>This study presents a family of non-symmetric, explicit six-point block methods of sixth order for solving second-order ordinary and partial differential equations. The construction focuses on reducing phase and amplification errors to improve performance in oscillatory and dissipative problems. The order, phase-error behavior, and stability properties of the methods are analyzed, and their stability regions are illustrated. Numerical experiments on benchmark ODE and PDE problems confirm that the proposed schemes deliver higher accuracy. Comparisons with 12-step explicit symplectic Runge–Kutta methods and trigonometric-fitted schemes further show that the new methods are computationally faster.</p>

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A Novel Amplification-Fitted and Phase Controlled 6-Point Block Method for Second-Order Oscillatory Problems

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Mei Hong,
  • Chia-Liang Lin,
  • Anurag Kaur,
  • Theodore E. Simos

摘要

This study presents a family of non-symmetric, explicit six-point block methods of sixth order for solving second-order ordinary and partial differential equations. The construction focuses on reducing phase and amplification errors to improve performance in oscillatory and dissipative problems. The order, phase-error behavior, and stability properties of the methods are analyzed, and their stability regions are illustrated. Numerical experiments on benchmark ODE and PDE problems confirm that the proposed schemes deliver higher accuracy. Comparisons with 12-step explicit symplectic Runge–Kutta methods and trigonometric-fitted schemes further show that the new methods are computationally faster.