Time domain integral equation modeling based on ordinary differential equation solution methods

A new set of methods for solving the time domain integral equations of electromagnetic theory is introduced. Rather than using a Galerkin space-time discretization, the new approach couples a Galerkin spatial discretization with temporal integrations based on ordinary differential equation techniques. The new temporal discretization method can easily model dispersion, gives rise to high-order convergence, and results in a method that is absolutely stable for any time step. Numerical results will demonstrate the convergence, accuracy, and stability of the technique for a variety of problems.