Numerical treatment and analysis of time-fractional evolution equations:
This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type eit...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2023]
|
| Schriftenreihe: | Applied mathematical sciences
214 |
| Schlagworte: | |
| Zusammenfassung: | This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis--back cover |
| Beschreibung: | xiii, 427 Seiten 25 cm |
| ISBN: | 3031210492 9783031210495 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV048879892 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 230328s2023 b||| 00||| eng d | ||
| 020 | |a 3031210492 |9 3031210492 | ||
| 020 | |a 9783031210495 |9 9783031210495 | ||
| 035 | |a (OCoLC)1374569781 | ||
| 035 | |a (DE-599)BVBBV048879892 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 | ||
| 100 | 1 | |a Jin, Bangti |e Verfasser |0 (DE-588)1065640293 |4 aut | |
| 245 | 1 | 0 | |a Numerical treatment and analysis of time-fractional evolution equations |c Bangti Jin, Zhi Zhou |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2023] | |
| 300 | |a xiii, 427 Seiten |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 336 | |b sti |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 214 | |
| 505 | 8 | |a 1. Existence, Uniqueness, and Regularity of Solutions -- 2. Spatially Semidiscrete Discretization -- 3. Convolution Quadrature -- 4. Finite Difference Methods: Construction and Implementation -- 5. Finite Difference Methods on Uniform Meshes -- 6. Finite Difference Methods on Graded Meshes -- 7. Nonnegativity Preservation -- 8. Discrete Maximal Regularity -- 9. Subdiffusion with Time-Dependent Coefficients -- 10. Semilinear Subdiffusion -- 11. Time-Space Finite Element Approximation -- 12. Spectral Galerkin Approximation -- 13. Incomplete Iterative Solution at Time Levels -- 14. Optimal Control with Subdiffusion Constraint -- 15. Backward Subdiffusion -- Appendix A: Mathematical Preliminaries -- References -- Index | |
| 520 | 3 | |a This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis--back cover | |
| 653 | 0 | |a Evolution equations | |
| 653 | 0 | |a Fractional differential equations | |
| 653 | 0 | |a Evolution equations | |
| 653 | 0 | |a Fractional differential equations | |
| 700 | 1 | |a Zhou, Zhi |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-21050-1 |
| 830 | 0 | |a Applied mathematical sciences |v 214 |w (DE-604)BV000005274 |9 214 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-034144646 | ||
Datensatz im Suchindex
| _version_ | 1804185024623280128 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Jin, Bangti |
| author_GND | (DE-588)1065640293 |
| author_facet | Jin, Bangti |
| author_role | aut |
| author_sort | Jin, Bangti |
| author_variant | b j bj |
| building | Verbundindex |
| bvnumber | BV048879892 |
| contents | 1. Existence, Uniqueness, and Regularity of Solutions -- 2. Spatially Semidiscrete Discretization -- 3. Convolution Quadrature -- 4. Finite Difference Methods: Construction and Implementation -- 5. Finite Difference Methods on Uniform Meshes -- 6. Finite Difference Methods on Graded Meshes -- 7. Nonnegativity Preservation -- 8. Discrete Maximal Regularity -- 9. Subdiffusion with Time-Dependent Coefficients -- 10. Semilinear Subdiffusion -- 11. Time-Space Finite Element Approximation -- 12. Spectral Galerkin Approximation -- 13. Incomplete Iterative Solution at Time Levels -- 14. Optimal Control with Subdiffusion Constraint -- 15. Backward Subdiffusion -- Appendix A: Mathematical Preliminaries -- References -- Index |
| ctrlnum | (OCoLC)1374569781 (DE-599)BVBBV048879892 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02900nam a2200397 cb4500</leader><controlfield tag="001">BV048879892</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">230328s2023 b||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3031210492</subfield><subfield code="9">3031210492</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783031210495</subfield><subfield code="9">9783031210495</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1374569781</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV048879892</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jin, Bangti</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1065640293</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical treatment and analysis of time-fractional evolution equations</subfield><subfield code="c">Bangti Jin, Zhi Zhou</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham, Switzerland</subfield><subfield code="b">Springer</subfield><subfield code="c">[2023]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiii, 427 Seiten</subfield><subfield code="c">25 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">sti</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applied mathematical sciences</subfield><subfield code="v">214</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">1. Existence, Uniqueness, and Regularity of Solutions -- 2. Spatially Semidiscrete Discretization -- 3. Convolution Quadrature -- 4. Finite Difference Methods: Construction and Implementation -- 5. Finite Difference Methods on Uniform Meshes -- 6. Finite Difference Methods on Graded Meshes -- 7. Nonnegativity Preservation -- 8. Discrete Maximal Regularity -- 9. Subdiffusion with Time-Dependent Coefficients -- 10. Semilinear Subdiffusion -- 11. Time-Space Finite Element Approximation -- 12. Spectral Galerkin Approximation -- 13. Incomplete Iterative Solution at Time Levels -- 14. Optimal Control with Subdiffusion Constraint -- 15. Backward Subdiffusion -- Appendix A: Mathematical Preliminaries -- References -- Index</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis--back cover</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Evolution equations</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Fractional differential equations</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Evolution equations</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Fractional differential equations</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhou, Zhi</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-031-21050-1</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applied mathematical sciences</subfield><subfield code="v">214</subfield><subfield code="w">(DE-604)BV000005274</subfield><subfield code="9">214</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-034144646</subfield></datafield></record></collection> |
| id | DE-604.BV048879892 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:45:54Z |
| indexdate | 2024-07-10T09:48:39Z |
| institution | BVB |
| isbn | 3031210492 9783031210495 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034144646 |
| oclc_num | 1374569781 |
| open_access_boolean | |
| owner | DE-20 |
| owner_facet | DE-20 |
| physical | xiii, 427 Seiten 25 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Jin, Bangti Verfasser (DE-588)1065640293 aut Numerical treatment and analysis of time-fractional evolution equations Bangti Jin, Zhi Zhou Cham, Switzerland Springer [2023] xiii, 427 Seiten 25 cm txt rdacontent sti rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 214 1. Existence, Uniqueness, and Regularity of Solutions -- 2. Spatially Semidiscrete Discretization -- 3. Convolution Quadrature -- 4. Finite Difference Methods: Construction and Implementation -- 5. Finite Difference Methods on Uniform Meshes -- 6. Finite Difference Methods on Graded Meshes -- 7. Nonnegativity Preservation -- 8. Discrete Maximal Regularity -- 9. Subdiffusion with Time-Dependent Coefficients -- 10. Semilinear Subdiffusion -- 11. Time-Space Finite Element Approximation -- 12. Spectral Galerkin Approximation -- 13. Incomplete Iterative Solution at Time Levels -- 14. Optimal Control with Subdiffusion Constraint -- 15. Backward Subdiffusion -- Appendix A: Mathematical Preliminaries -- References -- Index This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis--back cover Evolution equations Fractional differential equations Zhou, Zhi Sonstige oth Erscheint auch als Online-Ausgabe 978-3-031-21050-1 Applied mathematical sciences 214 (DE-604)BV000005274 214 |
| spellingShingle | Jin, Bangti Numerical treatment and analysis of time-fractional evolution equations Applied mathematical sciences 1. Existence, Uniqueness, and Regularity of Solutions -- 2. Spatially Semidiscrete Discretization -- 3. Convolution Quadrature -- 4. Finite Difference Methods: Construction and Implementation -- 5. Finite Difference Methods on Uniform Meshes -- 6. Finite Difference Methods on Graded Meshes -- 7. Nonnegativity Preservation -- 8. Discrete Maximal Regularity -- 9. Subdiffusion with Time-Dependent Coefficients -- 10. Semilinear Subdiffusion -- 11. Time-Space Finite Element Approximation -- 12. Spectral Galerkin Approximation -- 13. Incomplete Iterative Solution at Time Levels -- 14. Optimal Control with Subdiffusion Constraint -- 15. Backward Subdiffusion -- Appendix A: Mathematical Preliminaries -- References -- Index |
| title | Numerical treatment and analysis of time-fractional evolution equations |
| title_auth | Numerical treatment and analysis of time-fractional evolution equations |
| title_exact_search | Numerical treatment and analysis of time-fractional evolution equations |
| title_exact_search_txtP | Numerical treatment and analysis of time-fractional evolution equations |
| title_full | Numerical treatment and analysis of time-fractional evolution equations Bangti Jin, Zhi Zhou |
| title_fullStr | Numerical treatment and analysis of time-fractional evolution equations Bangti Jin, Zhi Zhou |
| title_full_unstemmed | Numerical treatment and analysis of time-fractional evolution equations Bangti Jin, Zhi Zhou |
| title_short | Numerical treatment and analysis of time-fractional evolution equations |
| title_sort | numerical treatment and analysis of time fractional evolution equations |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT jinbangti numericaltreatmentandanalysisoftimefractionalevolutionequations AT zhouzhi numericaltreatmentandanalysisoftimefractionalevolutionequations |