Implicit Runge-Kutta Methods for the Discretization of Time Domain Integral Equations

Implicit Runge-Kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory. The proposed technique maps a Laplace-domain equation to a Ƶ-domain equation using the Butcher tableau of the implicit Runge-Kutta scheme. A discrete time domain system is recovered by computing the inverse Ƶ-transform numerically. The resulting technique is capable of third- or fifth-order accuracy in time, and is stable independent of time step. Numerical results illustrate the accuracy and stability of the technique.