Two space dimensional hyperbolic equations with variable coefficients via meshless local Petrov-Galerkin method

In this work, a two dimensional linear hyperbolic equations with variable coefficients will be solved using the local Petrov-Galerkin method based on radial basis functions. Since the coefficients of differential operators are variable, the use of Green s theorem requires special treatments. The radial point interpolation method is used to construct shape functions. For time discretization, a Crank-Nicolson finite difference scheme is employed. To illustrate the efficiency and accuracy of the proposed method, a numerical example is presented.