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<p>In this work, we investigate the Klein–Gordon equation, a physical problem, using the reproducing kernel Hilbert space method (RKHSM). The analytical solution is expressed as a series within the reproducing kernel Hilbert space (RKHS). The proposed approach leverages the RKHSM to approximate solutions, alongside reproducing kernel functions. Numerical examples are provided to demonstrate the accuracy and effectiveness of this method. A comparison between the exact solutions and those obtained through the proposed method highlights its simplicity and reliability.</p>

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Numerical technique for solving physical models using reproducing kernel Hilbert space method with purely integral conditions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月27日

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  • Hadjer Zerouali,
  • Nourhane Attia,
  • Ali Akgül,
  • Ahcene Merad,
  • Douha Saadi,
  • Evren Hincal,
  • Murad Khan Hassani

摘要

In this work, we investigate the Klein–Gordon equation, a physical problem, using the reproducing kernel Hilbert space method (RKHSM). The analytical solution is expressed as a series within the reproducing kernel Hilbert space (RKHS). The proposed approach leverages the RKHSM to approximate solutions, alongside reproducing kernel functions. Numerical examples are provided to demonstrate the accuracy and effectiveness of this method. A comparison between the exact solutions and those obtained through the proposed method highlights its simplicity and reliability.