### Abstract

A numerical method for two-point boundary value problems with constant coefficients is developed which is based on integral equations and the spectral integration matrix for Chebyshev nodes. The method is stable, achieves superalgebraic convergence, and requires O(N log N) operations, where N is the number of nodes in the discretization. Although stable spectral methods have been constructed in the past, they have generally been based on reformulating the recurrence relations obtained through spectral differentiation in an attempt to avoid the ill-conditioning introduced by that process.

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

Pages (from-to) | 1071-1080 |

Number of pages | 10 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 28 |

Issue number | 4 |

State | Published - Aug 1991 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*28*(4), 1071-1080.

**Spectral integration and two-point boundary value problems.** / Greengard, Leslie.

Research output: Contribution to journal › Article

*SIAM Journal on Numerical Analysis*, vol. 28, no. 4, pp. 1071-1080.

}

TY - JOUR

T1 - Spectral integration and two-point boundary value problems

AU - Greengard, Leslie

PY - 1991/8

Y1 - 1991/8

N2 - A numerical method for two-point boundary value problems with constant coefficients is developed which is based on integral equations and the spectral integration matrix for Chebyshev nodes. The method is stable, achieves superalgebraic convergence, and requires O(N log N) operations, where N is the number of nodes in the discretization. Although stable spectral methods have been constructed in the past, they have generally been based on reformulating the recurrence relations obtained through spectral differentiation in an attempt to avoid the ill-conditioning introduced by that process.

AB - A numerical method for two-point boundary value problems with constant coefficients is developed which is based on integral equations and the spectral integration matrix for Chebyshev nodes. The method is stable, achieves superalgebraic convergence, and requires O(N log N) operations, where N is the number of nodes in the discretization. Although stable spectral methods have been constructed in the past, they have generally been based on reformulating the recurrence relations obtained through spectral differentiation in an attempt to avoid the ill-conditioning introduced by that process.

UR - http://www.scopus.com/inward/record.url?scp=0026202215&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026202215&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026202215

VL - 28

SP - 1071

EP - 1080

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 4

ER -