Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods
Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the B...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
INAN, BILGE [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
exponential finite difference method |
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| Anmerkung: |
© Indian Academy of Sciences 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Pramāna - Springer India, 1973, 81(2013), 4 vom: 21. Sept., Seite 547-556 |
|---|---|
| Übergeordnetes Werk: |
volume:81 ; year:2013 ; number:4 ; day:21 ; month:09 ; pages:547-556 |
| Links: |
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| DOI / URN: |
10.1007/s12043-013-0599-z |
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OLC2076062122 |
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| 520 | |a Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. | ||
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10.1007/s12043-013-0599-z doi (DE-627)OLC2076062122 (DE-He213)s12043-013-0599-z-p DE-627 ger DE-627 rakwb eng 530 VZ INAN, BILGE verfasserin aut Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Academy of Sciences 2013 Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. Burgers’ equation exponential finite difference method implicit exponential finite difference method fully implicit exponential finite difference method BAHADIR, AHMET REFIK aut Enthalten in Pramāna Springer India, 1973 81(2013), 4 vom: 21. Sept., Seite 547-556 (DE-627)129403342 (DE-600)186949-8 (DE-576)014785102 0304-4289 nnns volume:81 year:2013 number:4 day:21 month:09 pages:547-556 https://doi.org/10.1007/s12043-013-0599-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 81 2013 4 21 09 547-556 |
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10.1007/s12043-013-0599-z doi (DE-627)OLC2076062122 (DE-He213)s12043-013-0599-z-p DE-627 ger DE-627 rakwb eng 530 VZ INAN, BILGE verfasserin aut Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Academy of Sciences 2013 Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. Burgers’ equation exponential finite difference method implicit exponential finite difference method fully implicit exponential finite difference method BAHADIR, AHMET REFIK aut Enthalten in Pramāna Springer India, 1973 81(2013), 4 vom: 21. Sept., Seite 547-556 (DE-627)129403342 (DE-600)186949-8 (DE-576)014785102 0304-4289 nnns volume:81 year:2013 number:4 day:21 month:09 pages:547-556 https://doi.org/10.1007/s12043-013-0599-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 81 2013 4 21 09 547-556 |
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10.1007/s12043-013-0599-z doi (DE-627)OLC2076062122 (DE-He213)s12043-013-0599-z-p DE-627 ger DE-627 rakwb eng 530 VZ INAN, BILGE verfasserin aut Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Indian Academy of Sciences 2013 Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. Burgers’ equation exponential finite difference method implicit exponential finite difference method fully implicit exponential finite difference method BAHADIR, AHMET REFIK aut Enthalten in Pramāna Springer India, 1973 81(2013), 4 vom: 21. Sept., Seite 547-556 (DE-627)129403342 (DE-600)186949-8 (DE-576)014785102 0304-4289 nnns volume:81 year:2013 number:4 day:21 month:09 pages:547-556 https://doi.org/10.1007/s12043-013-0599-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 81 2013 4 21 09 547-556 |
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Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods |
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Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. © Indian Academy of Sciences 2013 |
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Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. © Indian Academy of Sciences 2013 |
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Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. © Indian Academy of Sciences 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2076062122</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230402043012.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12043-013-0599-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2076062122</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s12043-013-0599-z-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">INAN, BILGE</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Indian Academy of Sciences 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. 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The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Burgers’ equation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">exponential finite difference method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">implicit exponential finite difference method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">fully implicit exponential finite difference method</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">BAHADIR, AHMET REFIK</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Pramāna</subfield><subfield code="d">Springer India, 1973</subfield><subfield code="g">81(2013), 4 vom: 21. Sept., Seite 547-556</subfield><subfield code="w">(DE-627)129403342</subfield><subfield code="w">(DE-600)186949-8</subfield><subfield code="w">(DE-576)014785102</subfield><subfield code="x">0304-4289</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:81</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:4</subfield><subfield code="g">day:21</subfield><subfield code="g">month:09</subfield><subfield code="g">pages:547-556</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s12043-013-0599-z</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">81</subfield><subfield code="j">2013</subfield><subfield code="e">4</subfield><subfield code="b">21</subfield><subfield code="c">09</subfield><subfield code="h">547-556</subfield></datafield></record></collection>
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