Quintic Hermite Spline Collocation Approach to the Time Fractional RLW and MRLW equations

This study presents a quintic Hermite spline-based collocation scheme for solving the Regularized Long-Wave (RLW) and Modified RLW equations in both integer-order and Caputo time-fractional settings. To the best of our knowledge, this represents the first application of this technique to these specific equations. Using Legendre and Chebyshev collocation points, the method is rigorously assessed through benchmark problems. A von Neumann analysis confirms the unconditional stability of the linearized scheme. Numerical results demonstrate that the proposed approach yields superior accuracy compared to existing methods, achieving high precision even on coarse spatial meshes. Additionally, the algorithm’s conservative nature is verified by the preservation of mass, momentum, and energy invariants. The findings establish the method as a robust and efficient framework for simulating complex fractional wave dynamics.