A Novel Conservative Compact Difference Scheme With High‐Order Accuracy for the Regularized Long‐Wave Equation

ABSTRACT In this work, we introduce a new high‐order compact finite difference method tailored for the numerical resolution of the regularized long wave (RLW) equation. The designed scheme respects two discrete conservation properties. We establish the unique solvability of the method and prove that it is unconditionally stable and converges. The scheme achieves second‐order accuracy in time and sixth‐order accuracy in space under the norm. To evaluate its performance, we consider benchmark problems, including the evolution of a single soliton and the interaction between multiple solitons. The preservation of three conserved quantities is investigated to validate the conservation behavior of the method. Additionally, we apply the scheme to a Maxwellian‐type initial pulse. Comparative analysis with other existing approaches confirms the precision and robustness of the proposed technique.