A hybrid numerical method for a two-dimensional second order hyperbolic equation

Abstract

Second order hyperbolic differential equations have been used to model many problems that appear related to heat conduction, mass diffusion and fluid dynamics. In this work a numerical method is presented to solve a two dimensional second order hyperbolic equation with convection terms. A hybrid numerical method is considered which consists of applying the Laplace transform in time and a finite volume discretization in space, where the shape functions associated with the finite volume method are chosen as the combination of hyperbolic functions. We present some numerical tests to show the efficiency of the numerical method.