Numerical investigation of the dispersive long wave equation using an adaptive moving mesh method and its stability

Abstract

This paper investigates the exact and numerical solutions of the dispersive long wave equations (DLWE) using the extended Jacobian elliptic function expansion method (EJEFET) and the adaptive moving mesh method (AMMT). The uniform mesh method (UMM) is also applied to obtain some numerical results. The analysis of the stability of these solutions is also presented. The achieved solutions are stable. We compare both numerical and exact solutions and obtained that the numerical results are accurate. Some 3D figures are plotted to reinforce and ensure the integrity of the qualitative and quantitative results obtained in this work. Finally, L2 and L∞ errors are analyzed to discover the proper performance of the considered techniques in solving DLWE.

Keywords

• Dispersive long wave equation
• Extended Jacobian elliptic function expansion method
• Adaptive moving mesh method
• MMPDEs