## Abstract

We develop end analyze a family of mappings which enhance the accuracy of Chebyshev pseudo-spectral methods in approximating functions with multiple regions of localized rapid variation (layers). The mapping family depends on 3N − 1 free parameters, where N is the number of layers. N parameters depend upon the locations of the layers and on the widths of the layers, while the other N − 1 parameters depend on the resolution of each layer relative to the first layer. The parameters can be determined adaptively by minimizing a functional which measures the error of the approximation. Techniques to simplify the minimization process are developed. We further demonstrate that the appropriate choice of mappings can lead to a significant reduction in the condition number of matrices associated with Chebyshev pseudo-spectral differentation. We illustrate the effectiveness of the proposed mapping and adaptive procedure by examples in which we approximate (i) given functions exhibiting multiple layers and (ii) the solution of a system of partial differential equations modeling combustion in counterflowing jets so that two distinct flames occur.

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

Pages (from-to) | 160-172 |

Number of pages | 13 |

Journal | Journal of Computational Physics |

Volume | 116 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1995 |

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics