Fast algorithm for calculation of the moving tsunami wave height

One of the most urgent problems of mathematical tsunami modeling is estimation of a tsunami wave height while a wave approaches to the coastal zone. There are two methods for solving this problem, namely, Airy–Green formula in one-dimensional case
$$ S^{(l)}(x)=S^{(l)}(0)\cdot\root4\of{H(0)/H(x)}, $$
and numerical solution of an initial-boundary value problem for linear shallow water equations (LSWE) that depends on three variables. The main difficulty problem of tsunami modeling is a very big size of the computational domain. The calculation of the solution of LSWE (the function of three variables) in this domain requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height for linear source which is based on kinematic-type approach and analytical representation of fundamental solution of LSWE. We get the expression of the moving tsunami wave height for the point source and demonstrate connections between tsunami amplitude for point, linear and arbitrary sources.