Efficient numerical scheme based on the method of lines for the shallow water equations

In this paper, a nonlinear shallow-water model of tsunami wave propagation at different points along a coastline of an ocean has been numerically simulated using method of lines. The simulation is carried out for various coastal slopes and the ocean depths. The effects of the coast slope and sea depth on the tsunami wave run-up height and velocity are illustrated. The accuracy of the mathematical model is verified by solving a classical test problem with known analytic solution. The computed run-up height and velocity show satisfactory agreement with the tsunami wave physics.