Solution of Ordinary Differential Equations with MathLie View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1999

AUTHORS

Gerd Baumann

ABSTRACT

This article discusses Lie’s method of canonical variables to solve ordinary differential equations. The method of canonical variables is based on point symmetries and allows to construct transformations which simplify the equation prior to its solution. The method of canonical variables is closely related to the methods of first integrals and the method of first order partial differential equations. We discuss the necessary tools, the skeleton and the class of solution, providing the solution in connection with computer algebra. The procedure of canonical variables is algorithmic and implemented in MathLie. We demonstrate the application of the method on first- and second-order ordinary differential equations. More... »

PAGES

1-23

References to SciGraph publications

Book

TITLE

Computer Algebra in Scientific Computing CASC’99

ISBN

978-3-540-66047-7
978-3-642-60218-4

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-60218-4_1

DOI

http://dx.doi.org/10.1007/978-3-642-60218-4_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1042026683


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Ulm", 
          "id": "https://www.grid.ac/institutes/grid.6582.9", 
          "name": [
            "Department of Mathematical Physics, University of Ulm, D-89069\u00a0Ulm, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Baumann", 
        "givenName": "Gerd", 
        "id": "sg:person.01247751074.51", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01247751074.51"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/s0010-4655(97)00018-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004982347"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf03026611", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028012043", 
          "https://doi.org/10.1007/bf03026611"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0305-4470/29/5/013", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059075246"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1999", 
    "datePublishedReg": "1999-01-01", 
    "description": "This article discusses Lie\u2019s method of canonical variables to solve ordinary differential equations. The method of canonical variables is based on point symmetries and allows to construct transformations which simplify the equation prior to its solution. The method of canonical variables is closely related to the methods of first integrals and the method of first order partial differential equations. We discuss the necessary tools, the skeleton and the class of solution, providing the solution in connection with computer algebra. The procedure of canonical variables is algorithmic and implemented in MathLie. We demonstrate the application of the method on first- and second-order ordinary differential equations.", 
    "editor": [
      {
        "familyName": "Ganzha", 
        "givenName": "Victor G.", 
        "type": "Person"
      }, 
      {
        "familyName": "Mayr", 
        "givenName": "Ernst W.", 
        "type": "Person"
      }, 
      {
        "familyName": "Vorozhtsov", 
        "givenName": "Evgenii V.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-642-60218-4_1", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-540-66047-7", 
        "978-3-642-60218-4"
      ], 
      "name": "Computer Algebra in Scientific Computing CASC\u201999", 
      "type": "Book"
    }, 
    "name": "Solution of Ordinary Differential Equations with MathLie", 
    "pagination": "1-23", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-642-60218-4_1"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "c831c86f699e3f6fb5ebd8122bb2263c97f37268845c8e5842d6db2bf4aec894"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1042026683"
        ]
      }
    ], 
    "publisher": {
      "location": "Berlin, Heidelberg", 
      "name": "Springer Berlin Heidelberg", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-642-60218-4_1", 
      "https://app.dimensions.ai/details/publication/pub.1042026683"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T23:54", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8697_00000269.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-3-642-60218-4_1"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-60218-4_1'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-60218-4_1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-60218-4_1'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-60218-4_1'


 

This table displays all metadata directly associated to this object as RDF triples.

85 TRIPLES      23 PREDICATES      30 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-642-60218-4_1 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N13f59e8e5a5c4bfda416fada3794ef26
4 schema:citation sg:pub.10.1007/bf03026611
5 https://doi.org/10.1016/s0010-4655(97)00018-0
6 https://doi.org/10.1088/0305-4470/29/5/013
7 schema:datePublished 1999
8 schema:datePublishedReg 1999-01-01
9 schema:description This article discusses Lie’s method of canonical variables to solve ordinary differential equations. The method of canonical variables is based on point symmetries and allows to construct transformations which simplify the equation prior to its solution. The method of canonical variables is closely related to the methods of first integrals and the method of first order partial differential equations. We discuss the necessary tools, the skeleton and the class of solution, providing the solution in connection with computer algebra. The procedure of canonical variables is algorithmic and implemented in MathLie. We demonstrate the application of the method on first- and second-order ordinary differential equations.
10 schema:editor N2d257bae90014eb1a4d43404b4a42fbe
11 schema:genre chapter
12 schema:inLanguage en
13 schema:isAccessibleForFree false
14 schema:isPartOf N2f108569b8454d778b6a3b02154f1a4e
15 schema:name Solution of Ordinary Differential Equations with MathLie
16 schema:pagination 1-23
17 schema:productId N3cb1a08cc8824960856d7e6aacc42e6f
18 N5b5e50daa915477ba7bdd4518e033895
19 Ne5a7b108d1744d63bbe2dfdc8fbd86be
20 schema:publisher Nab1984e697cd4b449aeddda320218f0f
21 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042026683
22 https://doi.org/10.1007/978-3-642-60218-4_1
23 schema:sdDatePublished 2019-04-15T23:54
24 schema:sdLicense https://scigraph.springernature.com/explorer/license/
25 schema:sdPublisher N74bdcf9844b84078970699efc3cfda50
26 schema:url http://link.springer.com/10.1007/978-3-642-60218-4_1
27 sgo:license sg:explorer/license/
28 sgo:sdDataset chapters
29 rdf:type schema:Chapter
30 N00a3ca864f2f431d992a5e00404523a5 schema:familyName Vorozhtsov
31 schema:givenName Evgenii V.
32 rdf:type schema:Person
33 N113ca84679a84e80bf6f1bb7d8a0db02 rdf:first Nafdfc21025ca4df48ece88fb0ad01f38
34 rdf:rest Ne72a1e5d7a9f41de86c375bdd9ca7f3d
35 N13f59e8e5a5c4bfda416fada3794ef26 rdf:first sg:person.01247751074.51
36 rdf:rest rdf:nil
37 N2d257bae90014eb1a4d43404b4a42fbe rdf:first N947719d909e84ccfaa7d843323bc7c33
38 rdf:rest N113ca84679a84e80bf6f1bb7d8a0db02
39 N2f108569b8454d778b6a3b02154f1a4e schema:isbn 978-3-540-66047-7
40 978-3-642-60218-4
41 schema:name Computer Algebra in Scientific Computing CASC’99
42 rdf:type schema:Book
43 N3cb1a08cc8824960856d7e6aacc42e6f schema:name readcube_id
44 schema:value c831c86f699e3f6fb5ebd8122bb2263c97f37268845c8e5842d6db2bf4aec894
45 rdf:type schema:PropertyValue
46 N5b5e50daa915477ba7bdd4518e033895 schema:name dimensions_id
47 schema:value pub.1042026683
48 rdf:type schema:PropertyValue
49 N74bdcf9844b84078970699efc3cfda50 schema:name Springer Nature - SN SciGraph project
50 rdf:type schema:Organization
51 N947719d909e84ccfaa7d843323bc7c33 schema:familyName Ganzha
52 schema:givenName Victor G.
53 rdf:type schema:Person
54 Nab1984e697cd4b449aeddda320218f0f schema:location Berlin, Heidelberg
55 schema:name Springer Berlin Heidelberg
56 rdf:type schema:Organisation
57 Nafdfc21025ca4df48ece88fb0ad01f38 schema:familyName Mayr
58 schema:givenName Ernst W.
59 rdf:type schema:Person
60 Ne5a7b108d1744d63bbe2dfdc8fbd86be schema:name doi
61 schema:value 10.1007/978-3-642-60218-4_1
62 rdf:type schema:PropertyValue
63 Ne72a1e5d7a9f41de86c375bdd9ca7f3d rdf:first N00a3ca864f2f431d992a5e00404523a5
64 rdf:rest rdf:nil
65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
66 schema:name Mathematical Sciences
67 rdf:type schema:DefinedTerm
68 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
69 schema:name Pure Mathematics
70 rdf:type schema:DefinedTerm
71 sg:person.01247751074.51 schema:affiliation https://www.grid.ac/institutes/grid.6582.9
72 schema:familyName Baumann
73 schema:givenName Gerd
74 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01247751074.51
75 rdf:type schema:Person
76 sg:pub.10.1007/bf03026611 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028012043
77 https://doi.org/10.1007/bf03026611
78 rdf:type schema:CreativeWork
79 https://doi.org/10.1016/s0010-4655(97)00018-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004982347
80 rdf:type schema:CreativeWork
81 https://doi.org/10.1088/0305-4470/29/5/013 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059075246
82 rdf:type schema:CreativeWork
83 https://www.grid.ac/institutes/grid.6582.9 schema:alternateName University of Ulm
84 schema:name Department of Mathematical Physics, University of Ulm, D-89069 Ulm, Germany
85 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...