### Abstract

Language | English |
---|---|

Title of host publication | Mathematical and numerical aspects of wave propagation phenomena |

Place of Publication | London, UK |

Publisher | Springer |

Pages | 770-775 |

Number of pages | 5 |

ISBN (Print) | 354040127X |

Publication status | Published - 2003 |

### Fingerprint

### Keywords

- wave propagation
- mathematics
- integral equations

### Cite this

*Mathematical and numerical aspects of wave propagation phenomena*(pp. 770-775). London, UK: Springer.

}

*Mathematical and numerical aspects of wave propagation phenomena.*Springer, London, UK, pp. 770-775.

**Convergence of a collocation scheme for a retarded potential integral equation.** / Duncan, D.B.; Cohen, Gary (Editor); Heikkola, E. (Editor); Joly, Patrick (Editor); Neittaanmäki, P. (Editor).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Convergence of a collocation scheme for a retarded potential integral equation

AU - Duncan, D.B.

A2 - Cohen, Gary

A2 - Heikkola, E.

A2 - Joly, Patrick

A2 - Neittaanmäki, P.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - wave propagation

KW - mathematics

KW - integral equations

M3 - Chapter

SN - 354040127X

SP - 770

EP - 775

BT - Mathematical and numerical aspects of wave propagation phenomena

PB - Springer

CY - London, UK

ER -