Boundary element method and wave equation

In this paper the boundary integral expression for a one-dimensional wave equation with homogeneous boundary conditions is developed. This is done using the time dependent fundamental solution of the corresponding hyperbolic partial differential equation. The integral expression developed is a generalized function with the same form as the well-known D'Alembert formula. The derivatives of the solution and some useful invariants on the characteristics of the partial differential equation are also calculated.The boundary element method is applied to find the numerical solution. The results show excellent agreement with analytical solutions.A multi-step procedure for large time steps which can be used in the boundary element method is also described.In addition, the way in which boundary conditions are introduced during the time dependent process is explained in detail. In the Appendix the main properties of Dirac's delta function and the Heaviside unit step function are described.