DOI: 10.1007/bf01400309. Mesh selection for discrete solution of boundary problems in ordinary differential equations

Mesh selection for discrete solution of boundary problems in ordinary differential equations

10.1007/bf01400309

Crossref journal-article

Springer Science and Business Media LLC

Numerische Mathematik (297)

Bibliography

Pereyra, V., & Sewell, E. G. (1974). Mesh selection for discrete solution of boundary problems in ordinary differential equations. Numerische Mathematik, 23(3), 261â268.

Authors 2

V. Pereyra (first)
E. G. Sewell (additional)

References 15 Referenced 129

De Boor, C.: Good approximation by splines with variable knots. II. Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics363, 12–20. Berlin-Heidelberg-New York: Springer 1973 / Good approximation by splines with variable knots. II. Conference on the Numerical Solution of Differential Equations / Lecture Notes in Mathematics by C. De Boor (1973)
Brown, R. R.: Numerical solution of boundary value problems using nonuniform grids. J. SIAM10, 475–495 (1962) / J. SIAM by R. R. Brown (1962)
Denny, V. E., Landis, R. B.: A new method for solving two-point boundary value problems using optimal node destribution. J. Comp. Phys.9, 120–137 (1972) (10.1016/0021-9991(72)90039-3) / J. Comp. Phys. by V. E. Denny (1972)
Dodson, D. S.: Optimal order approximation by polynomial spline functions. Ph. D. Thesis, Purdue Univ., Lafayette, Ind. (1972) / Optimal order approximation by polynomial spline functions by D. S. Dodson (1972)
Keller, H. B.: Numerical methods for two-point boundary-value problems. Waltham, Mass.: Blaisdell 1968 / Numerical methods for two-point boundary-value problems by H. B. Keller (1968)
Keller, H. B.: Accurate difference methods for linear ordinary differential systems subject to linear constraints. SIAM J. Numer. Anal.6, 8–30 (1969) (10.1137/0706002) / SIAM J. Numer. Anal. by H. B. Keller (1969)
Keller, H. B.: Some new results on difference methods for two point boundary value problems. Actas, Seminario Métodos Numéricos Modernos I, pp. 63–82. Depto. de Comp., Fac. Ciencias, Univ. Central de Venezuela, Caracas (1974) / Some new results on difference methods for two point boundary value problems. Actas, Seminario Métodos Numéricos Modernos I by H. B. Keller (1974)
Lentini, M., Pereyra, V.: A variable order finite difference method for nonlinear multipoint boundary value problems. Pub. 73-06, Depto. de Comp., Fac. Ciencias, Univ. Central de Venezuela, Caracas (1973). To appear in Math. Comp. Oct. 1974 / A variable order finite difference method for nonlinear multipoint boundary value problems. Pub. 73-06 by M. Lentini (1973)
Lentini, M., Pereyra, V.: Boundary problem solvers for first order systems based on deferred corrections. Proceedings NSF Symposium, Numerical Solutions of Boundary Problems. Univ. of Maryland Baltimore City. (1974) (10.1016/B978-0-12-068660-5.50015-6)
Lentini, M., Pereyra, V.: An adaptive solver for nonlinear two-point first order system problems with mild boundary layers. In preparation
Pearson, C. E.: On a differential equation of boundary layer type. J. Math. Phys.47, 134–154 (1968) (10.1002/sapm1968471134) / J. Math. Phys. by C. E. Pearson (1968)
Pereyra, V.: Iterated deferred corrections for nonlinear operator equations. Numer. Math.10, 316–323 (1967) (10.1007/BF02162030) / Numer. Math. by V. Pereyra (1967)
Pereyra, V.: Variable order variable step finite difference methods for nonlinear boundary value problems. Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics363, 118–133. Berlin: Springer 1973 / Variable order variable step finite difference methods for nonlinear boundary value problems / Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics by V. Pereyra (1973)
Sewell, E. G.: Automatic generation of triangulations for piecewise polynomial approximation. Ph. D. Thesis, Purdue Univ., Lafayette, Ind. (1972) / Automatic generation of triangulations for piecewise polynomial approximation by E. G. Sewell (1972)
Burchard, H. G.: Splines (with optimal knots) are better. J. App. Anal.3, 309–319 (1974) (10.1080/00036817408839073) / J. App. Anal. by H. G. Burchard (1974)

Dates

Type	When
Created	20 years, 4 months ago (April 2, 2005, 12:10 p.m.)
Deposited	1 year, 11 months ago (Sept. 13, 2023, 9:55 a.m.)
Indexed	1 month, 1 week ago (July 22, 2025, 7:12 a.m.)
Issued	51 years, 2 months ago (June 1, 1974)
Published	51 years, 2 months ago (June 1, 1974)
Published Print	51 years, 2 months ago (June 1, 1974)

Funders 0

None

BibTeX

@article{Pereyra_1974, title={Mesh selection for discrete solution of boundary problems in ordinary differential equations}, volume={23}, ISSN={0945-3245}, url={http://dx.doi.org/10.1007/bf01400309}, DOI={10.1007/bf01400309}, number={3}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Pereyra, V. and Sewell, E. G.}, year={1974}, month=jun, pages={261–268} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        22
      ]
    ],
    "date-time": "2025-07-22T11:12:22Z",
    "timestamp": 1753182742568
  },
  "reference-count": 15,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "3",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1974,
            6,
            1
          ]
        ],
        "date-time": "1974-06-01T00:00:00Z",
        "timestamp": 139276800000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://www.springernature.com/gp/researchers/text-and-data-mining"
    },
    {
      "start": {
        "date-parts": [
          [
            1974,
            6,
            1
          ]
        ],
        "date-time": "1974-06-01T00:00:00Z",
        "timestamp": 139276800000
      },
      "content-version": "vor",
      "delay-in-days": 0,
      "URL": "https://www.springernature.com/gp/researchers/text-and-data-mining"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1974,
        6
      ]
    ]
  },
  "DOI": "10.1007/bf01400309",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        4,
        2
      ]
    ],
    "date-time": "2005-04-02T17:10:46Z",
    "timestamp": 1112461846000
  },
  "page": "261-268",
  "source": "Crossref",
  "is-referenced-by-count": 129,
  "title": "Mesh selection for discrete solution of boundary problems in ordinary differential equations",
  "prefix": "10.1007",
  "volume": "23",
  "author": [
    {
      "given": "V.",
      "family": "Pereyra",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "E. G.",
      "family": "Sewell",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "BF01400309_CR1",
      "series-title": "Lecture Notes in Mathematics",
      "first-page": "12",
      "volume-title": "Good approximation by splines with variable knots. II. Conference on the Numerical Solution of Differential Equations",
      "author": "C. De Boor",
      "year": "1973",
      "unstructured": "De Boor, C.: Good approximation by splines with variable knots. II. Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics363, 12\u201320. Berlin-Heidelberg-New York: Springer 1973"
    },
    {
      "key": "BF01400309_CR2",
      "first-page": "475",
      "volume": "10",
      "author": "R. R. Brown",
      "year": "1962",
      "unstructured": "Brown, R. R.: Numerical solution of boundary value problems using nonuniform grids. J. SIAM10, 475\u2013495 (1962)",
      "journal-title": "J. SIAM"
    },
    {
      "key": "BF01400309_CR3",
      "doi-asserted-by": "crossref",
      "first-page": "120",
      "DOI": "10.1016/0021-9991(72)90039-3",
      "volume": "9",
      "author": "V. E. Denny",
      "year": "1972",
      "unstructured": "Denny, V. E., Landis, R. B.: A new method for solving two-point boundary value problems using optimal node destribution. J. Comp. Phys.9, 120\u2013137 (1972)",
      "journal-title": "J. Comp. Phys."
    },
    {
      "key": "BF01400309_CR4",
      "volume-title": "Optimal order approximation by polynomial spline functions",
      "author": "D. S. Dodson",
      "year": "1972",
      "unstructured": "Dodson, D. S.: Optimal order approximation by polynomial spline functions. Ph. D. Thesis, Purdue Univ., Lafayette, Ind. (1972)"
    },
    {
      "key": "BF01400309_CR5",
      "volume-title": "Numerical methods for two-point boundary-value problems",
      "author": "H. B. Keller",
      "year": "1968",
      "unstructured": "Keller, H. B.: Numerical methods for two-point boundary-value problems. Waltham, Mass.: Blaisdell 1968"
    },
    {
      "key": "BF01400309_CR6",
      "doi-asserted-by": "crossref",
      "first-page": "8",
      "DOI": "10.1137/0706002",
      "volume": "6",
      "author": "H. B. Keller",
      "year": "1969",
      "unstructured": "Keller, H. B.: Accurate difference methods for linear ordinary differential systems subject to linear constraints. SIAM J. Numer. Anal.6, 8\u201330 (1969)",
      "journal-title": "SIAM J. Numer. Anal."
    },
    {
      "key": "BF01400309_CR7",
      "first-page": "63",
      "volume-title": "Some new results on difference methods for two point boundary value problems. Actas, Seminario M\u00e9todos Num\u00e9ricos Modernos I",
      "author": "H. B. Keller",
      "year": "1974",
      "unstructured": "Keller, H. B.: Some new results on difference methods for two point boundary value problems. Actas, Seminario M\u00e9todos Num\u00e9ricos Modernos I, pp. 63\u201382. Depto. de Comp., Fac. Ciencias, Univ. Central de Venezuela, Caracas (1974)"
    },
    {
      "key": "BF01400309_CR8",
      "volume-title": "A variable order finite difference method for nonlinear multipoint boundary value problems. Pub. 73-06",
      "author": "M. Lentini",
      "year": "1973",
      "unstructured": "Lentini, M., Pereyra, V.: A variable order finite difference method for nonlinear multipoint boundary value problems. Pub. 73-06, Depto. de Comp., Fac. Ciencias, Univ. Central de Venezuela, Caracas (1973). To appear in Math. Comp. Oct. 1974"
    },
    {
      "key": "BF01400309_CR9",
      "doi-asserted-by": "crossref",
      "unstructured": "Lentini, M., Pereyra, V.: Boundary problem solvers for first order systems based on deferred corrections. Proceedings NSF Symposium, Numerical Solutions of Boundary Problems. Univ. of Maryland Baltimore City. (1974)",
      "DOI": "10.1016/B978-0-12-068660-5.50015-6"
    },
    {
      "key": "BF01400309_CR10",
      "unstructured": "Lentini, M., Pereyra, V.: An adaptive solver for nonlinear two-point first order system problems with mild boundary layers. In preparation"
    },
    {
      "key": "BF01400309_CR11",
      "doi-asserted-by": "crossref",
      "first-page": "134",
      "DOI": "10.1002/sapm1968471134",
      "volume": "47",
      "author": "C. E. Pearson",
      "year": "1968",
      "unstructured": "Pearson, C. E.: On a differential equation of boundary layer type. J. Math. Phys.47, 134\u2013154 (1968)",
      "journal-title": "J. Math. Phys."
    },
    {
      "key": "BF01400309_CR12",
      "doi-asserted-by": "crossref",
      "first-page": "316",
      "DOI": "10.1007/BF02162030",
      "volume": "10",
      "author": "V. Pereyra",
      "year": "1967",
      "unstructured": "Pereyra, V.: Iterated deferred corrections for nonlinear operator equations. Numer. Math.10, 316\u2013323 (1967)",
      "journal-title": "Numer. Math."
    },
    {
      "key": "BF01400309_CR13",
      "series-title": "Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics",
      "first-page": "118",
      "volume-title": "Variable order variable step finite difference methods for nonlinear boundary value problems",
      "author": "V. Pereyra",
      "year": "1973",
      "unstructured": "Pereyra, V.: Variable order variable step finite difference methods for nonlinear boundary value problems. Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics363, 118\u2013133. Berlin: Springer 1973"
    },
    {
      "key": "BF01400309_CR14",
      "volume-title": "Automatic generation of triangulations for piecewise polynomial approximation",
      "author": "E. G. Sewell",
      "year": "1972",
      "unstructured": "Sewell, E. G.: Automatic generation of triangulations for piecewise polynomial approximation. Ph. D. Thesis, Purdue Univ., Lafayette, Ind. (1972)"
    },
    {
      "key": "BF01400309_CR15",
      "doi-asserted-by": "crossref",
      "first-page": "309",
      "DOI": "10.1080/00036817408839073",
      "volume": "3",
      "author": "H. G. Burchard",
      "year": "1974",
      "unstructured": "Burchard, H. G.: Splines (with optimal knots) are better. J. App. Anal.3, 309\u2013319 (1974)",
      "journal-title": "J. App. Anal."
    }
  ],
  "container-title": "Numerische Mathematik",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://link.springer.com/content/pdf/10.1007/BF01400309.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://link.springer.com/article/10.1007/BF01400309/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01400309",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    },
    {
      "URL": "https://link.springer.com/content/pdf/10.1007/BF01400309.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        9,
        13
      ]
    ],
    "date-time": "2023-09-13T13:55:36Z",
    "timestamp": 1694613336000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://link.springer.com/10.1007/BF01400309"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1974,
        6
      ]
    ]
  },
  "references-count": 15,
  "journal-issue": {
    "issue": "3",
    "published-print": {
      "date-parts": [
        [
          1974,
          6
        ]
      ]
    }
  },
  "alternative-id": [
    "BF01400309"
  ],
  "URL": "http://dx.doi.org/10.1007/BF01400309",
  "relation": {},
  "ISSN": [
    "0029-599X",
    "0945-3245"
  ],
  "subject": [],
  "container-title-short": "Numer. Math.",
  "published": {
    "date-parts": [
      [
        1974,
        6
      ]
    ]
  }
}