Generalized finite difference/spectral Galerkin approximations for the time-fractional telegraph equation View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-09-12

AUTHORS

Ying Wang, Liquan Mei

ABSTRACT

We discuss the numerical solution of the time-fractional telegraph equation. The main purpose of this work is to construct and analyze stable and high-order scheme for solving the time-fractional telegraph equation efficiently. The proposed method is based on a generalized finite difference scheme in time and Legendre spectral Galerkin method in space. Stability and convergence of the method are established rigorously. We prove that the temporal discretization scheme is unconditionally stable and the numerical solution converges to the exact one with order O(τ2−α+N1−ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {O}(\tau^{2-\alpha}+N^{1-\omega})$\end{document}, where τ,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau, N $\end{document}, and ω are the time step size, polynomial degree, and regularity of the exact solution, respectively. Numerical experiments are carried out to verify the theoretical claims. More... »

PAGES

281

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13662-017-1348-2

DOI

http://dx.doi.org/10.1186/s13662-017-1348-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1091608923


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xianning West Road, Xi\u2019an, People\u2019s Republic of China", 
          "id": "http://www.grid.ac/institutes/grid.43169.39", 
          "name": [
            "School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xianning West Road, Xi\u2019an, People\u2019s Republic of China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Wang", 
        "givenName": "Ying", 
        "id": "sg:person.016217246055.58", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016217246055.58"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xianning West Road, Xi\u2019an, People\u2019s Republic of China", 
          "id": "http://www.grid.ac/institutes/grid.43169.39", 
          "name": [
            "School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xianning West Road, Xi\u2019an, People\u2019s Republic of China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Mei", 
        "givenName": "Liquan", 
        "id": "sg:person.014733412147.03", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014733412147.03"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s10092-013-0084-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046667870", 
          "https://doi.org/10.1007/s10092-013-0084-6"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2017-09-12", 
    "datePublishedReg": "2017-09-12", 
    "description": "We discuss the numerical solution of the time-fractional telegraph equation. The main purpose of this work is to construct and analyze stable and high-order scheme for solving the time-fractional telegraph equation efficiently. The proposed method is based on a generalized finite difference scheme in time and Legendre spectral Galerkin method in space. Stability and convergence of the method are established rigorously. We prove that the temporal discretization scheme is unconditionally stable and the numerical solution converges to the exact one with order O(\u03c42\u2212\u03b1+N1\u2212\u03c9)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathcal {O}(\\tau^{2-\\alpha}+N^{1-\\omega})$\\end{document}, where \u03c4,N\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\tau, N $\\end{document}, and \u03c9 are the time step size, polynomial degree, and regularity of the exact solution, respectively. Numerical experiments are carried out to verify the theoretical claims.", 
    "genre": "article", 
    "id": "sg:pub.10.1186/s13662-017-1348-2", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1052613", 
        "issn": [
          "1687-1839", 
          "2731-4235"
        ], 
        "name": "Advances in Continuous and Discrete Models", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2017"
      }
    ], 
    "keywords": [
      "time-fractional telegraph equation", 
      "telegraph equation", 
      "generalized finite difference scheme", 
      "Legendre spectral Galerkin method", 
      "spectral Galerkin approximations", 
      "spectral Galerkin method", 
      "numerical solution converges", 
      "finite difference scheme", 
      "high-order schemes", 
      "temporal discretization schemes", 
      "time step size", 
      "Galerkin approximation", 
      "difference scheme", 
      "discretization scheme", 
      "exact solution", 
      "solution converges", 
      "numerical solution", 
      "Galerkin method", 
      "polynomial degree", 
      "numerical experiments", 
      "step size", 
      "equations", 
      "theoretical claims", 
      "scheme", 
      "approximation", 
      "solution", 
      "converges", 
      "convergence", 
      "main purpose", 
      "space", 
      "regularity", 
      "stability", 
      "order", 
      "work", 
      "experiments", 
      "size", 
      "time", 
      "degree", 
      "purpose", 
      "claims", 
      "method"
    ], 
    "name": "Generalized finite difference/spectral Galerkin approximations for the time-fractional telegraph equation", 
    "pagination": "281", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1091608923"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1186/s13662-017-1348-2"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1186/s13662-017-1348-2", 
      "https://app.dimensions.ai/details/publication/pub.1091608923"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-11-24T21:01", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221124/entities/gbq_results/article/article_742.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1186/s13662-017-1348-2"
  }
]
 

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.10.1186/s13662-017-1348-2'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s13662-017-1348-2'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s13662-017-1348-2'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s13662-017-1348-2'


 

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

109 TRIPLES      21 PREDICATES      66 URIs      57 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1186/s13662-017-1348-2 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author Ndaba34881a0a45d08c61d7538fcff3bd
4 schema:citation sg:pub.10.1007/s10092-013-0084-6
5 schema:datePublished 2017-09-12
6 schema:datePublishedReg 2017-09-12
7 schema:description We discuss the numerical solution of the time-fractional telegraph equation. The main purpose of this work is to construct and analyze stable and high-order scheme for solving the time-fractional telegraph equation efficiently. The proposed method is based on a generalized finite difference scheme in time and Legendre spectral Galerkin method in space. Stability and convergence of the method are established rigorously. We prove that the temporal discretization scheme is unconditionally stable and the numerical solution converges to the exact one with order O(τ2−α+N1−ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {O}(\tau^{2-\alpha}+N^{1-\omega})$\end{document}, where τ,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau, N $\end{document}, and ω are the time step size, polynomial degree, and regularity of the exact solution, respectively. Numerical experiments are carried out to verify the theoretical claims.
8 schema:genre article
9 schema:isAccessibleForFree true
10 schema:isPartOf N64d50c60bf6b48c6bc5a5e6d4e8debd3
11 Nb639507d360b482e9287fb99c7c2064c
12 sg:journal.1052613
13 schema:keywords Galerkin approximation
14 Galerkin method
15 Legendre spectral Galerkin method
16 approximation
17 claims
18 convergence
19 converges
20 degree
21 difference scheme
22 discretization scheme
23 equations
24 exact solution
25 experiments
26 finite difference scheme
27 generalized finite difference scheme
28 high-order schemes
29 main purpose
30 method
31 numerical experiments
32 numerical solution
33 numerical solution converges
34 order
35 polynomial degree
36 purpose
37 regularity
38 scheme
39 size
40 solution
41 solution converges
42 space
43 spectral Galerkin approximations
44 spectral Galerkin method
45 stability
46 step size
47 telegraph equation
48 temporal discretization schemes
49 theoretical claims
50 time
51 time step size
52 time-fractional telegraph equation
53 work
54 schema:name Generalized finite difference/spectral Galerkin approximations for the time-fractional telegraph equation
55 schema:pagination 281
56 schema:productId N881e00257aa04ea498c1a8188e39a34f
57 N95ba01ad3adb4fc9927e329336d3a951
58 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091608923
59 https://doi.org/10.1186/s13662-017-1348-2
60 schema:sdDatePublished 2022-11-24T21:01
61 schema:sdLicense https://scigraph.springernature.com/explorer/license/
62 schema:sdPublisher Ncf92ae8e0b244b8d957d5f59f4bc6449
63 schema:url https://doi.org/10.1186/s13662-017-1348-2
64 sgo:license sg:explorer/license/
65 sgo:sdDataset articles
66 rdf:type schema:ScholarlyArticle
67 N64d50c60bf6b48c6bc5a5e6d4e8debd3 schema:volumeNumber 2017
68 rdf:type schema:PublicationVolume
69 N881e00257aa04ea498c1a8188e39a34f schema:name doi
70 schema:value 10.1186/s13662-017-1348-2
71 rdf:type schema:PropertyValue
72 N95ba01ad3adb4fc9927e329336d3a951 schema:name dimensions_id
73 schema:value pub.1091608923
74 rdf:type schema:PropertyValue
75 N99352eb177044e20be51711174d1d6a3 rdf:first sg:person.014733412147.03
76 rdf:rest rdf:nil
77 Nb639507d360b482e9287fb99c7c2064c schema:issueNumber 1
78 rdf:type schema:PublicationIssue
79 Ncf92ae8e0b244b8d957d5f59f4bc6449 schema:name Springer Nature - SN SciGraph project
80 rdf:type schema:Organization
81 Ndaba34881a0a45d08c61d7538fcff3bd rdf:first sg:person.016217246055.58
82 rdf:rest N99352eb177044e20be51711174d1d6a3
83 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
84 schema:name Mathematical Sciences
85 rdf:type schema:DefinedTerm
86 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
87 schema:name Numerical and Computational Mathematics
88 rdf:type schema:DefinedTerm
89 sg:journal.1052613 schema:issn 1687-1839
90 2731-4235
91 schema:name Advances in Continuous and Discrete Models
92 schema:publisher Springer Nature
93 rdf:type schema:Periodical
94 sg:person.014733412147.03 schema:affiliation grid-institutes:grid.43169.39
95 schema:familyName Mei
96 schema:givenName Liquan
97 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014733412147.03
98 rdf:type schema:Person
99 sg:person.016217246055.58 schema:affiliation grid-institutes:grid.43169.39
100 schema:familyName Wang
101 schema:givenName Ying
102 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016217246055.58
103 rdf:type schema:Person
104 sg:pub.10.1007/s10092-013-0084-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046667870
105 https://doi.org/10.1007/s10092-013-0084-6
106 rdf:type schema:CreativeWork
107 grid-institutes:grid.43169.39 schema:alternateName School of Mathematics and Statistics, Xi’an Jiaotong University, Xianning West Road, Xi’an, People’s Republic of China
108 schema:name School of Mathematics and Statistics, Xi’an Jiaotong University, Xianning West Road, Xi’an, People’s Republic of China
109 rdf:type schema:Organization
 




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


...