Mathematical modeling of tsunami wave propagation at mid ocean and its amplification and run-up on shore

• Solution of the mathematical model of tsunami wave by Elzaki Adomian Decomposition Method has been studied. • How tsunami wave velocity and run-up height are affected by the coast slope and sea depth are demonstrated. • It can be deduced from this work that, as the tsunami approaches the shore, its velocity reduces and the wave amplitude shoots up initially and then as the wave approaches the coastline, it decreases due to shoaling. • The result shows that the speed and height of tsunami waves are inversely proportional to the depth of the ocean. The paper deals with the study of the mathematical model of tsunami wave propagation along a coastline of an ocean. The model is based on shallow-water assumption which is represented by a system of non-linear partial differential equations. In this study, we employ the Elzaki Adomian Decomposition Method (EADM) to successfully obtain the solution for the proposed model for different coastal slopes and ocean depths. How tsunami wave velocity and run-up height are affected by the coast slope and sea depth are demonstrated. The Adomian Decomposition Method together with Elzaki transform allows for solutions, without the need of any linearization or perturbation, in the form of rapidly converging series. The obtained numerical results for tsunami wave height and velocity are very close match to the real physical phenomenon of tsunami.