Subdivision collocation method for numerical treatment of regularized long wave (RLW) equation

Abstract

This research project introduces a novel computational approach for solving the regularized long wave equation. The proposed method utilizes a subdivision scheme with appropriate basis functions to transform the equation into a system of linear algebraic equations. A suitable numerical technique is employed to compute the solution of the transformed equations. Theoretical analysis of stability and error for the proposed method is also conducted. Furthermore, the invariants of three physical properties, waves, mass (M), momentum (P), and energy (e), are calculated. Additionally, numerical evidence is presented to demonstrate the effectiveness and accuracy of the method. The results of the numerical experiments confirm the efficiency and high accuracy of the proposed method. Moreover, the numerical results of the invariants validate the conservation laws and align with the theoretical results.