Picture of two heads

Open Access research that challenges the mind...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including those from the School of Psychological Sciences & Health - but also papers by researchers based within the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

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

[img]
Preview
PDF
131665_.pdf - Preprint

Download (192kB) | Preview

Abstract

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.