Title: | The numerical solution of boundary-value problems for differential equations with state dependent deviating arguments (English) |

Author: | Bakke, Vernon L. |

Author: | Jackiewicz, Zdzisław |

Language: | English |

Journal: | Aplikace matematiky |

ISSN: | 0373-6725 |

Volume: | 34 |

Issue: | 1 |

Year: | 1989 |

Pages: | 1-17 |

Summary lang: | English |

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Category: | math |

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Summary: | A numerical method for the solution of a second order boundary value problem for differential equation with state dependent deviating argument is studied. Second-order convergence is established and a theorem about the asymptotic expansion of global discretization error is given. This theorem makes it possible to improve the accuracy of the numerical solution by using Richardson extrapolation which results in a convergent method of order three. This is in contrast to boundary value problems for ordinary differential equations where the use of Richardson extrapolation results in a method of order four. (English) |

Keyword: | second order |

Keyword: | difference operator |

Keyword: | second order convergence |

Keyword: | asymptotic expansion |

Keyword: | global discretization error |

Keyword: | numerical examples |

Keyword: | boundary value problem |

Keyword: | deviating argument |

Keyword: | Richardson extrapolation |

Keyword: | convergence of higher order |

MSC: | 34K10 |

MSC: | 65L10 |

idZBL: | Zbl 0669.65065 |

idMR: | MR0982339 |

DOI: | 10.21136/AM.1989.104330 |

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Date available: | 2008-05-20T18:35:47Z |

Last updated: | 2020-07-28 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/104330 |

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Reference: | [1] V. L. Bakke Z. Jackiewicz: A note on the numerical computation of solutions to second order boundary value problems with state dependent deviating arguments.University of Arkansas Numerical Analysis Technical Report 65110-1, June, 1985. |

Reference: | [2] B. Chartres R. Stepleman: Convergence of difference methods for initial and boundary value problems with discontinuous data.Math. Соmр., v. 25, 1971, pp. 724-732. MR 0303739 |

Reference: | [3] P. Chocholaty L. Slahor: A numerical method to boundary value problems for second order delay-differential equations.Numer. Math., v. 33, 1979, pp. 69-75. MR 0545743, 10.1007/BF01396496 |

Reference: | [4] K. De Nevers K. Schmitt: An application of the shooting method to boundary value problems for second order delay equations.J. Math. Anal. Appl., v. 36, 1971, pp. 588-597. MR 0298166, 10.1016/0022-247X(71)90041-2 |

Reference: | [5] L. J. Grimm K. Schmitt: Boundary value problems for delay-differential equations.Bull. Amer. Math. Soc., v. 74, 1968, pp. 997-1000. MR 0228785, 10.1090/S0002-9904-1968-12114-7 |

Reference: | [6] L. J. Grimm K. Schmitt: Boundary value problems for differential equations with deviating arguments.Aequationes Math., v. 4, 1970, p. 176-190. MR 0262632, 10.1007/BF01817758 |

Reference: | [7] G. A. Kamenskii S. B. Norkin L. E. Eľsgoľts: Some directions of investigation on the theory of differential equations with deviating arguments.(Russian). Trudy Sem. Tear. Diff. Urav. Otklon. Arg., v. 6, pp. 3-36. |

Reference: | [8] H. B. Keller: Numerical methods for two-point boundary-value problems.Blaisdel Publishing Company, Waltham 1968. Zbl 0172.19503, MR 0230476 |

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