NUMERICAL STABILITY AND CONVERGENCE OF APPROXIMATIONS OF RETARDED POTENTIAL INTEGRAL-EQUATIONS

Stability and convergence results for approximations of retarded potential integral equations are given. Such integral approximations arise in time marching schemes for direct scattering problems, and are both extremely complicated and computationally intensive. They are often observed to have exponentially increasing unstable solutions. A stability analysis is performed which is shown to provide a way of predicting whether a given scheme is stable or not. The proposed test is supported by numerical experiments and requires much less computation than the scheme itself. It is also shown that if an approximation for this type of integral equation is both stable and consistent, then it is convergent.