Kirli, EmreMersin, Mehmet Ali2025-04-222025-04-22202523495103https://dx.doi.org/10.1007/s40819-025-01832-xhttps://hdl.handle.net/20.500.12451/13119This study presents the application of a numerical method specifically designed to solve the Modified Regularized Long Wave equation, a crucial model in the analysis of non-linear wave dynamics. The proposed method employs a Quartic Trigonometric B-spline approach for spatial discretization, which ensures smooth and accurate interpolation across the spatial domain, while temporal integration is conducted using the well-established fourth-order Runge–Kutta (RK4) scheme, known for its stability and precision. To evaluate the performance of the method, it is applied to three test problems: the propagation of a single solitary wave, the interaction between two and three solitary waves. The invariant quantities are computed for all test cases. To ensure the stability of the method, a stability analysis is performed through the computation of eigenvalues. The results demonstrate that the proposed method achieves a high degree of accuracy in preserving the invariant properties and produces minimal error, highlighting its efficiency and reliability.eninfo:eu-repo/semantics/closedAccessModified Regularized Long WaveQuartic Trigonometric B-splineRunge KuttaSolitary WaveArticle11210.1007/s40819-025-01832-x2-s2.0-85218269776Q2