### Abstract

In this paper, we present a new numerical method for the solution of linear two‐point boundary value problems of ordinary differential equations. After reducing the differential equation to a second kind integral equation, we discretize the latter via a high order Nyström scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using O (N·p^{2}) operations, where N is the number of nodes on the interval and p is the desired order of convergence. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to end‐point singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods.

Original language | English (US) |
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Pages (from-to) | 419-452 |

Number of pages | 34 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 44 |

Issue number | 4 |

DOIs | |

State | Published - Jun 1991 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*44*(4), 419-452. https://doi.org/10.1002/cpa.3160440403