### Abstract

We present a fast algorithm for the evaluation of the exact nonreflecting boundary conditions for the Schrödinger equation in one dimension. The exact nonreflecting boundary condition contains a nonlocal term which is a convolution integral in time, with a kernel proportional to 1/√t. The key observation is that this integral can be split into two parts: a local part and a history part, each of which allows for separate treatment. The local part is computed by a quadrature suited for square-root singularities. For the history part, we approximate the convolution kernel uniformly by a sum of exponentials. The integral can then be evaluated recursively. As a result, the computation of the nonreflecting boundary conditions is both accurate and efficient.

Original language | English (US) |
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Pages (from-to) | 955-966 |

Number of pages | 12 |

Journal | Computers and Mathematics with Applications |

Volume | 47 |

Issue number | 6-7 |

DOIs | |

State | Published - 2004 |

### Keywords

- Fast algorithm
- Nonreflecting boundary condition
- Schrödinger equation

### ASJC Scopus subject areas

- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics