Two efficient numerical techniques for solutions of fractional shallow water equation

Abstract

In this paper, the nonlinear shallow water equation appears in the mathematical modeling of tsunami wave propagation along the coastline of an ocean is solved numerically. The model investigates fractional derivatives and is presented through a system of nonlinear partial differential equations. The variational iteration method (VIM) and the residual power series method (RPSM) have been applied to the fractional system of equations for different parameters. In addition, tsunami wave velocity and run-up height with respect to coast slope and sea depth are analyzed for different time and order in detail. A detailed error analysis is presented for tsunami velocity and tsunami wave propagation. The results obtained are compared to other existing results to show the efficiency and reliability of the proposed methods.

Keywords

• Shallow water equation
• Variational iteration method
• Liouville–Caputo fractional derivative
• Numerical solution
• Residual power series method
• Error analysis