DOI: 10.54974/fcmathsci.1872022 ISSN: 2717-6185

Approximate Solution of Time-Fractional Kawahara Equation Using the RBF Collocation Technique

Bahar Karaman, Emrah Karaman, Yılmaz Dereli
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The paper presents an approximate solution to the time-fractional Kawahara equation (TFKE), marking a significant advancement in the field. We decisively utilize the Liouville-Caputo fractional derivative (FD) as the foundation of our analytical framework. To discretize the equations in time, we expertly implement the Crank-Nicolson difference scheme, which guarantees precision and effectiveness. Additionally, we conduct a comprehensive stability analysis of the present scheme, applying the von-Neumann approach designed explicitly for fractional equations. The findings from the numerical experiments are clearly illustrated in the figures, effectively showcasing the robustness and reliability of our approach.

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