Boundary difference-integral equation method and its error estimates for second order hyperbolic partial differential equation (Q1314936)

The author advances a new method to solve the classical initial-boundary value problem for second order hyperbolic partial differential equations (actually wave equations) on a bounded or unbounded domain in 3D. He couples the finite difference method with the boundary integral equation method. Thus, by replacing the time derivatives by a difference quotient he changes the hyperbolic equation into an elliptic equation (more exactly a Dirichlet problem for the Helmholtz equation). Then, with the fundamental solution of this last equation, he obtains an approximate solution by the boundary finite element method. Proofs of existence and uniqueness are carried out as well as error estimates in energy norm and local maximum norms for the approximate solution.