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

This is the authors' abstract. We don't add key points for this paper.

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.