Numerical Simulation of Nonlinear Propagation of Tsunamis
In this thesis we study tsunami waves using nonlinear propagation. We start with a system of ordinary differential equations describing wave behavior and find an exact solution to the system. We use the Euler method to approximate the system and test it against the exact solution. We further use the "Leap-Frog" and 4th Order Runge-Kutta to approximate the system and test those results against the exact solution. We confirm the order of error of each of these methods. We start working with Fast Fourier Transforms to develop a special approximation method. Putting the methods together we can now approximate the wave in space and time. We test this approximation using a traveling wave because we can test it against an exact solution. In the second part of this thesis we introduce non-linearity into the program and add depth to the water which had been infinite before. Finally we take three tsunami waves and approximate their behavior.
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