### Abstract

An efficient L_{0}-stable parallel algorithm is developed for the two-dimensional diffusion equation with non-local time-dependent boundary conditions. The algorithm is based on subdiagonal Fade.́ approximation to the matrix exponentials arising from the use of the method of lines and may be implemented on a parallel architecture using two processors running concurrently with each processor employing the use of tridiagonal solvers at every time-step. The algorithm is tested on two model problems from the literature for which discontinuities between initial and boundary conditions exist. The CPU times together with the associated error estimates are compared.

Original language | English (US) |
---|---|

Pages (from-to) | 153-163 |

Number of pages | 11 |

Journal | International Journal of Computer Mathematics |

Volume | 64 |

Issue number | 1-2 |

State | Published - 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Fadé approximant
- L-stability
- Parallel algorithm

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*International Journal of Computer Mathematics*,

*64*(1-2), 153-163.

**Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass.** / Gumel, Abba; Ang, W. T.; Twizell, E. H.

Research output: Contribution to journal › Article

*International Journal of Computer Mathematics*, vol. 64, no. 1-2, pp. 153-163.

}

TY - JOUR

T1 - Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass

AU - Gumel, Abba

AU - Ang, W. T.

AU - Twizell, E. H.

PY - 1997

Y1 - 1997

N2 - An efficient L0-stable parallel algorithm is developed for the two-dimensional diffusion equation with non-local time-dependent boundary conditions. The algorithm is based on subdiagonal Fade.́ approximation to the matrix exponentials arising from the use of the method of lines and may be implemented on a parallel architecture using two processors running concurrently with each processor employing the use of tridiagonal solvers at every time-step. The algorithm is tested on two model problems from the literature for which discontinuities between initial and boundary conditions exist. The CPU times together with the associated error estimates are compared.

AB - An efficient L0-stable parallel algorithm is developed for the two-dimensional diffusion equation with non-local time-dependent boundary conditions. The algorithm is based on subdiagonal Fade.́ approximation to the matrix exponentials arising from the use of the method of lines and may be implemented on a parallel architecture using two processors running concurrently with each processor employing the use of tridiagonal solvers at every time-step. The algorithm is tested on two model problems from the literature for which discontinuities between initial and boundary conditions exist. The CPU times together with the associated error estimates are compared.

KW - Fadé approximant

KW - L-stability

KW - Parallel algorithm

UR - http://www.scopus.com/inward/record.url?scp=0030721325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030721325&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030721325

VL - 64

SP - 153

EP - 163

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 1-2

ER -