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

Stability and convergence results for approximations of retarded poten tial 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 ob served to have exponentially increasing unstable solutions. A stabilit y analysis is performed which is shown to provide a way of predicting whether a given scheme is stable or not. The proposed test is supporte d by numerical experiments and requires much less computation than the scheme itself. It is also shown that if an approximation for this typ e of integral equation is both stable and consistent, then it is conve rgent.