An Analytical and Numerical Approach to Solve the Tsunami Wave Propagation Equation (Contemporary Mathematics, 2025)
We study the mathematical model of tsunami wave propagation (TWP) along the coastline of an ocean. The described model is represented by a system of non-linear partial differential equations. In this study, we employ two different techniques: one is the Adomian decomposition method (ADM, which is an analytical approach), and another is the finite difference method (FDM, which is a numerical approach) to obtain the solution for the proposed TWP model successfully. The solutions gained are numerically represented in graphs and tables. The validity of the solutions is investigated by comparing this proposed method with the fractional reduced differential transform method (FRDTM). The novelty of this paper is that we have demonstrated that the numerical method (FDM) better approximates the solution of our partial differential equation than the analytical method (ADM), and this has not been explored before in any other works. We examine the velocity and height of the coastline of an ocean from the tsunami wave equation using numerical and analytical techniques. MATLAB and MAPLE are used to obtain numerical and graphical representations.
Keywords: tsunami model; FDM; ADM; non-linear partial differential equation