| Volume 15, Number 1, 2025, Pages - DOI：10.11948/JAAC-2024-0078 |
| Enhancing Solutions for Non-linear Ordinary Differential Equations via Combined Laplace Transform and Reproducing Kernel Method |
| Nourhane Attia,Ali Akgül |
| Keywords:Reproducing kernel method Laplace transformation Non-linear ODEs Numerical approximation |
| Abstract: |
| Ordinary differential equations encompass diverse phenomena in engineering and physics. This study aims to innovate by merging the Laplace transform operator with the reproducing kernel Hilbert space method (RKHSM), introducing an enhanced approach surpassing classical RKHSM. Employing the Laplace-RKHSM, we devise novel numerical solutions for non-linear ordinary differential equations, systematically yielding analytic and approximate solutions in series form. The effectiveness and efficacy of this new method are demonstrated through three applications, showcasing its performance. |
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