The boundary function method for singular perturbation problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
[1995]
|
| Schriftenreihe: | SIAM studies in applied mathematics
14 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (s. 209-217) and index Chapter 1: Basic ideas. Regular and singular perturbations; Asymptotic approximations; Asymptotic and convergent series; Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems -- Chapter 2: Singularly perturbed ordinary differential equations. Initial value problem; The critical case; Boundary value problems; Spike-type solutions and other contrast (dissipative) structures -- Chapter 3: Singularly perturbed partial differential equations. The method of Vishik-Lyusternik; Corner boundary functions; The smoothing procedure; Systems of equations in critical cases; Periodic solutions; Hyperbolic systems -- Chapter 4: Applied problems. Mathematical model of combustion process in the case of autocatalytic reaction; Heat conduction in thin bodies; Application of the boundary function method in the theory of semiconductor devices; Relaxation waves in the FitzHugh-Nagumo system; On some other applied problems -- Index This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology. The book also contains a variety of original ideas and explicit calculations previously available only in journal literature, as well as many concrete applied problems illustrating the boundary function method algorithms. Quite general asymptotic results described in the book are rigorous in the sense that, along with the asymptotic algorithms, in most cases the theorems on estimation of the remainder terms are presented. A survey of results of Russian mathematicians on the subject is provided; many of these results are not well known in the West. Based on the Russian edition of the textbook by Vasil'eva and Butuzov, this American edition, prepared by Kalachev, differs in many aspects. The text of the book has been revised substantially, some new material has been added to every chapter, and more examples, exercises, and new references on asymptotic methods and their applications have been included |
| Beschreibung: | 1 Online-Ressource (xiii, 221 Seiten) |
| ISBN: | 0898713331 9780898713336 |
| DOI: | 10.1137/1.9781611970784 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV039747232 | ||
| 003 | DE-604 | ||
| 005 | 20210408 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 111207s1995 sz |||| o||u| ||||||eng d | ||
| 010 | |a 94042996 | ||
| 020 | |a 0898713331 |c print |9 0898713331 | ||
| 020 | |a 9780898713336 |c print |9 9780898713336 | ||
| 020 | |z 9781611970784 |c electronic bk. |9 9781611970784 | ||
| 024 | 7 | |a 10.1137/1.9781611970784 |2 doi | |
| 035 | |a (OCoLC)873886331 | ||
| 035 | |a (DE-599)BVBBV039747232 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a sz |c XA-CH | ||
| 049 | |a DE-91 |a DE-29 |a DE-706 |a DE-83 |a DE-20 | ||
| 100 | 1 | |a Vasilʹeva, Adelaida Borisovna |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The boundary function method for singular perturbation problems |c Adelaida B. Vasilʹeva, Valentin F. Butuzov, and Leonid V. Kalachev |
| 264 | 1 | |a Philadelphia, Pa. |b Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) |c [1995] | |
| 264 | 4 | |c © 1995 | |
| 300 | |a 1 Online-Ressource (xiii, 221 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a SIAM studies in applied mathematics |v 14 | |
| 500 | |a Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader | ||
| 500 | |a Includes bibliographical references (s. 209-217) and index | ||
| 500 | |a Chapter 1: Basic ideas. Regular and singular perturbations; Asymptotic approximations; Asymptotic and convergent series; Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems -- Chapter 2: Singularly perturbed ordinary differential equations. Initial value problem; The critical case; Boundary value problems; Spike-type solutions and other contrast (dissipative) structures -- Chapter 3: Singularly perturbed partial differential equations. The method of Vishik-Lyusternik; Corner boundary functions; The smoothing procedure; Systems of equations in critical cases; Periodic solutions; Hyperbolic systems -- Chapter 4: Applied problems. Mathematical model of combustion process in the case of autocatalytic reaction; Heat conduction in thin bodies; Application of the boundary function method in the theory of semiconductor devices; Relaxation waves in the FitzHugh-Nagumo system; On some other applied problems -- Index | ||
| 500 | |a This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology. The book also contains a variety of original ideas and explicit calculations previously available only in journal literature, as well as many concrete applied problems illustrating the boundary function method algorithms. Quite general asymptotic results described in the book are rigorous in the sense that, along with the asymptotic algorithms, in most cases the theorems on estimation of the remainder terms are presented. A survey of results of Russian mathematicians on the subject is provided; many of these results are not well known in the West. Based on the Russian edition of the textbook by Vasil'eva and Butuzov, this American edition, prepared by Kalachev, differs in many aspects. The text of the book has been revised substantially, some new material has been added to every chapter, and more examples, exercises, and new references on asymptotic methods and their applications have been included | ||
| 650 | 4 | |a Boundary value problems / Numerical solutions | |
| 650 | 4 | |a Singular perturbations (Mathematics) | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Butuzov, V. F. |e Sonstige |4 oth | |
| 700 | 1 | |a Kalachev, Leonid V. |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 0898713331 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 9780898713336 |
| 830 | 0 | |a SIAM studies in applied mathematics |v 14 |w (DE-604)BV047229985 |9 14 | |
| 856 | 4 | 0 | |u https://doi.org/10.1137/1.9781611970784 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-72-SIA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024594763 | ||
| 966 | e | |u https://doi.org/10.1137/1.9781611970784 |l TUM01 |p ZDB-72-SIA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1137/1.9781611970784 |l UBW01 |p ZDB-72-SIA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1137/1.9781611970784 |l UBY01 |p ZDB-72-SIA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1137/1.9781611970784 |l UER01 |p ZDB-72-SIA |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804148637423370240 |
|---|---|
| any_adam_object | |
| author | Vasilʹeva, Adelaida Borisovna |
| author_facet | Vasilʹeva, Adelaida Borisovna |
| author_role | aut |
| author_sort | Vasilʹeva, Adelaida Borisovna |
| author_variant | a b v ab abv |
| building | Verbundindex |
| bvnumber | BV039747232 |
| collection | ZDB-72-SIA |
| ctrlnum | (OCoLC)873886331 (DE-599)BVBBV039747232 |
| doi_str_mv | 10.1137/1.9781611970784 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05030nmm a2200577zcb4500</leader><controlfield tag="001">BV039747232</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210408 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">111207s1995 sz |||| o||u| ||||||eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">94042996</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0898713331</subfield><subfield code="c">print</subfield><subfield code="9">0898713331</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780898713336</subfield><subfield code="c">print</subfield><subfield code="9">9780898713336</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781611970784</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">9781611970784</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1137/1.9781611970784</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)873886331</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV039747232</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="044" ind1=" " ind2=" "><subfield code="a">sz</subfield><subfield code="c">XA-CH</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Vasilʹeva, Adelaida Borisovna</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The boundary function method for singular perturbation problems</subfield><subfield code="c">Adelaida B. Vasilʹeva, Valentin F. Butuzov, and Leonid V. Kalachev</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Philadelphia, Pa.</subfield><subfield code="b">Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)</subfield><subfield code="c">[1995]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xiii, 221 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">SIAM studies in applied mathematics</subfield><subfield code="v">14</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (s. 209-217) and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Chapter 1: Basic ideas. Regular and singular perturbations; Asymptotic approximations; Asymptotic and convergent series; Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems -- Chapter 2: Singularly perturbed ordinary differential equations. Initial value problem; The critical case; Boundary value problems; Spike-type solutions and other contrast (dissipative) structures -- Chapter 3: Singularly perturbed partial differential equations. The method of Vishik-Lyusternik; Corner boundary functions; The smoothing procedure; Systems of equations in critical cases; Periodic solutions; Hyperbolic systems -- Chapter 4: Applied problems. Mathematical model of combustion process in the case of autocatalytic reaction; Heat conduction in thin bodies; Application of the boundary function method in the theory of semiconductor devices; Relaxation waves in the FitzHugh-Nagumo system; On some other applied problems -- Index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology. The book also contains a variety of original ideas and explicit calculations previously available only in journal literature, as well as many concrete applied problems illustrating the boundary function method algorithms. Quite general asymptotic results described in the book are rigorous in the sense that, along with the asymptotic algorithms, in most cases the theorems on estimation of the remainder terms are presented. A survey of results of Russian mathematicians on the subject is provided; many of these results are not well known in the West. Based on the Russian edition of the textbook by Vasil'eva and Butuzov, this American edition, prepared by Kalachev, differs in many aspects. The text of the book has been revised substantially, some new material has been added to every chapter, and more examples, exercises, and new references on asymptotic methods and their applications have been included</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Boundary value problems / Numerical solutions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Singular perturbations (Mathematics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Butuzov, V. F.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kalachev, Leonid V.</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">Druckausgabe</subfield><subfield code="z">0898713331</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">9780898713336</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">SIAM studies in applied mathematics</subfield><subfield code="v">14</subfield><subfield code="w">(DE-604)BV047229985</subfield><subfield code="9">14</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1137/1.9781611970784</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-72-SIA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-024594763</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970784</subfield><subfield code="l">TUM01</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970784</subfield><subfield code="l">UBW01</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970784</subfield><subfield code="l">UBY01</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1137/1.9781611970784</subfield><subfield code="l">UER01</subfield><subfield code="p">ZDB-72-SIA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV039747232 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:10:18Z |
| institution | BVB |
| isbn | 0898713331 9780898713336 |
| language | English |
| lccn | 94042996 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024594763 |
| oclc_num | 873886331 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-29 DE-706 DE-83 DE-20 |
| owner_facet | DE-91 DE-BY-TUM DE-29 DE-706 DE-83 DE-20 |
| physical | 1 Online-Ressource (xiii, 221 Seiten) |
| psigel | ZDB-72-SIA |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) |
| record_format | marc |
| series | SIAM studies in applied mathematics |
| series2 | SIAM studies in applied mathematics |
| spelling | Vasilʹeva, Adelaida Borisovna Verfasser aut The boundary function method for singular perturbation problems Adelaida B. Vasilʹeva, Valentin F. Butuzov, and Leonid V. Kalachev Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) [1995] © 1995 1 Online-Ressource (xiii, 221 Seiten) txt rdacontent c rdamedia cr rdacarrier SIAM studies in applied mathematics 14 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (s. 209-217) and index Chapter 1: Basic ideas. Regular and singular perturbations; Asymptotic approximations; Asymptotic and convergent series; Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems -- Chapter 2: Singularly perturbed ordinary differential equations. Initial value problem; The critical case; Boundary value problems; Spike-type solutions and other contrast (dissipative) structures -- Chapter 3: Singularly perturbed partial differential equations. The method of Vishik-Lyusternik; Corner boundary functions; The smoothing procedure; Systems of equations in critical cases; Periodic solutions; Hyperbolic systems -- Chapter 4: Applied problems. Mathematical model of combustion process in the case of autocatalytic reaction; Heat conduction in thin bodies; Application of the boundary function method in the theory of semiconductor devices; Relaxation waves in the FitzHugh-Nagumo system; On some other applied problems -- Index This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology. The book also contains a variety of original ideas and explicit calculations previously available only in journal literature, as well as many concrete applied problems illustrating the boundary function method algorithms. Quite general asymptotic results described in the book are rigorous in the sense that, along with the asymptotic algorithms, in most cases the theorems on estimation of the remainder terms are presented. A survey of results of Russian mathematicians on the subject is provided; many of these results are not well known in the West. Based on the Russian edition of the textbook by Vasil'eva and Butuzov, this American edition, prepared by Kalachev, differs in many aspects. The text of the book has been revised substantially, some new material has been added to every chapter, and more examples, exercises, and new references on asymptotic methods and their applications have been included Boundary value problems / Numerical solutions Singular perturbations (Mathematics) Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s DE-604 Butuzov, V. F. Sonstige oth Kalachev, Leonid V. Sonstige oth Erscheint auch als Druckausgabe 0898713331 Erscheint auch als Druckausgabe 9780898713336 SIAM studies in applied mathematics 14 (DE-604)BV047229985 14 https://doi.org/10.1137/1.9781611970784 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Vasilʹeva, Adelaida Borisovna The boundary function method for singular perturbation problems SIAM studies in applied mathematics Boundary value problems / Numerical solutions Singular perturbations (Mathematics) Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | The boundary function method for singular perturbation problems |
| title_auth | The boundary function method for singular perturbation problems |
| title_exact_search | The boundary function method for singular perturbation problems |
| title_full | The boundary function method for singular perturbation problems Adelaida B. Vasilʹeva, Valentin F. Butuzov, and Leonid V. Kalachev |
| title_fullStr | The boundary function method for singular perturbation problems Adelaida B. Vasilʹeva, Valentin F. Butuzov, and Leonid V. Kalachev |
| title_full_unstemmed | The boundary function method for singular perturbation problems Adelaida B. Vasilʹeva, Valentin F. Butuzov, and Leonid V. Kalachev |
| title_short | The boundary function method for singular perturbation problems |
| title_sort | the boundary function method for singular perturbation problems |
| topic | Boundary value problems / Numerical solutions Singular perturbations (Mathematics) Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Boundary value problems / Numerical solutions Singular perturbations (Mathematics) Randwertproblem |
| url | https://doi.org/10.1137/1.9781611970784 |
| volume_link | (DE-604)BV047229985 |
| work_keys_str_mv | AT vasilʹevaadelaidaborisovna theboundaryfunctionmethodforsingularperturbationproblems AT butuzovvf theboundaryfunctionmethodforsingularperturbationproblems AT kalachevleonidv theboundaryfunctionmethodforsingularperturbationproblems |