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Convergence of a collocation scheme for a retarded potential integral equation

Duncan, D.B. (2003) Convergence of a collocation scheme for a retarded potential integral equation. In: Mathematical and numerical aspects of wave propagation phenomena. Springer, London, UK, pp. 770-775. ISBN 354040127X

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Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. We shall describe some new stable collocation schemes and use Fourier methods and techniques from the analysis of one dimensional Volterra integral equations of the first kind to demonstrate that such stable schemes are convergent.