In this work, the two dimensional linear hyperbolic equations with variable coefficients will be solved using the local Petrov-Galerkin method based on radial basis functions. Due to the existence of variable coefficients for the differential operator, the use of Green's function requires special treatments. We use the radial point interpolation method to construct shape functions. For time discretization the finite difference and the Crank-Nicolson methods are employed to approximate the time and spacial derivatives respectively. A numerical example is presented to examine the efficiency and accuracy of the proposed method.
