Analysis of RLW and MRLW equation using an improvised collocation technique with SSP-RK43 scheme

Abstract

In this work, the regularized and the modified regularized long wave equations are solved using an improvised cubic B-spline collocation technique. Posteriori corrections are made in the cubic B-spline interpolant by forcing it to satisfy some specific interpolatory and end conditions, which results in the formation of improvised B-spline collocation technique. For temporal domain discretization, strong stability preserving Runge–Kutta scheme of third-order and four stages (SSP-RK43) is used. Seven important problems of the regularized and the modified regularized long wave equations are solved to demonstrate the applicability of the proposed technique. The motion of a single solitary wave, the interaction of two or more solitary waves, and the undulations of waves are shown graphically. These equations possess three invariants of motion namely mass, momentum, and energy, which need to remain constant with run time. For each problem, these invariants are calculated and it is observed that they coincide with exact values and remain preserved with time. The L2 and L∞ error norms are calculated at different time levels and CPU time is noted. Also, the stability analysis of the technique is carried out and is found to be conditionally stable.