Loading…
Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium
. In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equa...
Saved in:
| Published in: | European physical journal plus 2018-01, Vol.133 (1), p.28, Article 28 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c319t-58ee163f1ae9c69495364a42733aa00ce4e9c204e9ae1c02a171e35028bee2dc3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c319t-58ee163f1ae9c69495364a42733aa00ce4e9c204e9ae1c02a171e35028bee2dc3 |
| container_end_page | |
| container_issue | 1 |
| container_start_page | 28 |
| container_title | European physical journal plus |
| container_volume | 133 |
| creator | Parand, Kourosh Latifi, Sobhan Delkhosh, Mehdi Moayeri, Mohammad M. |
| description | .
In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval
[
0
,
∞
)
. Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope,
y
(
0
)
, is obtained as
-
1
.
191790649719421734122828603800159364
for
η
=
0
.
5
. Comparing to the best result obtained so far, it is accurate up to 36 decimal places. |
| doi_str_mv | 10.1140/epjp/i2018-11859-5 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2919732991</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2919732991</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-58ee163f1ae9c69495364a42733aa00ce4e9c204e9ae1c02a171e35028bee2dc3</originalsourceid><addsrcrecordid>eNp9UMFKAzEQXUTBov6Ap4Dn1UySbZujFK1KwYuew5idblN2kzXZFRT8d2Mr6Mk5zAyP994MryjOgV8CKH5F_ba_coLDvASYV7qsDoqJAM3LSil1-Gc_Ls5S2vJcSoPSalJ8LslTxNZ9UM1W2ET0jUPPHtCGF8eWOKbEbGjbYHFwwbOOhk2o2TpElkL75nzDRp8GwvqduRSGDcUOW9ZgYsMmhrHZMGSdszGUHn1gfchgyja1G7vT4miNbaKzn3lSPN_ePC3uytXj8n5xvSqtBD2U1ZwIpnINSNpOtdKVnCpUYiYlIueWVMYFzx0JLBcIMyBZcTF_IRK1lSfFxd63j-F1pDSYbRijzyeN0KBnUmgNmSX2rPxsSpHWpo-uw_hugJvvpM130maXtNklbaoskntRymTfUPy1_kf1Bd0zhZA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2919732991</pqid></control><display><type>article</type><title>Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium</title><source>Springer Nature</source><creator>Parand, Kourosh ; Latifi, Sobhan ; Delkhosh, Mehdi ; Moayeri, Mohammad M.</creator><creatorcontrib>Parand, Kourosh ; Latifi, Sobhan ; Delkhosh, Mehdi ; Moayeri, Mohammad M.</creatorcontrib><description>.
In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval
[
0
,
∞
)
. Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope,
y
(
0
)
, is obtained as
-
1
.
191790649719421734122828603800159364
for
η
=
0
.
5
. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/i2018-11859-5</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Accuracy ; Algebra ; Applied and Technical Physics ; Approximation ; Atomic ; Boundary conditions ; Collocation methods ; Complex Systems ; Condensed Matter Physics ; Decomposition ; Differential equations ; Engineering ; Investigations ; Mathematical and Computational Physics ; Methods ; Molecular ; Numerical analysis ; Optical and Plasma Physics ; Ordinary differential equations ; Partial differential equations ; Physics ; Physics and Astronomy ; Porous materials ; Porous media ; Regular Article ; Theoretical</subject><ispartof>European physical journal plus, 2018-01, Vol.133 (1), p.28, Article 28</ispartof><rights>Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-58ee163f1ae9c69495364a42733aa00ce4e9c204e9ae1c02a171e35028bee2dc3</citedby><cites>FETCH-LOGICAL-c319t-58ee163f1ae9c69495364a42733aa00ce4e9c204e9ae1c02a171e35028bee2dc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>Parand, Kourosh</creatorcontrib><creatorcontrib>Latifi, Sobhan</creatorcontrib><creatorcontrib>Delkhosh, Mehdi</creatorcontrib><creatorcontrib>Moayeri, Mohammad M.</creatorcontrib><title>Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>.
In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval
[
0
,
∞
)
. Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope,
y
(
0
)
, is obtained as
-
1
.
191790649719421734122828603800159364
for
η
=
0
.
5
. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.</description><subject>Accuracy</subject><subject>Algebra</subject><subject>Applied and Technical Physics</subject><subject>Approximation</subject><subject>Atomic</subject><subject>Boundary conditions</subject><subject>Collocation methods</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Decomposition</subject><subject>Differential equations</subject><subject>Engineering</subject><subject>Investigations</subject><subject>Mathematical and Computational Physics</subject><subject>Methods</subject><subject>Molecular</subject><subject>Numerical analysis</subject><subject>Optical and Plasma Physics</subject><subject>Ordinary differential equations</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Porous materials</subject><subject>Porous media</subject><subject>Regular Article</subject><subject>Theoretical</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9UMFKAzEQXUTBov6Ap4Dn1UySbZujFK1KwYuew5idblN2kzXZFRT8d2Mr6Mk5zAyP994MryjOgV8CKH5F_ba_coLDvASYV7qsDoqJAM3LSil1-Gc_Ls5S2vJcSoPSalJ8LslTxNZ9UM1W2ET0jUPPHtCGF8eWOKbEbGjbYHFwwbOOhk2o2TpElkL75nzDRp8GwvqduRSGDcUOW9ZgYsMmhrHZMGSdszGUHn1gfchgyja1G7vT4miNbaKzn3lSPN_ePC3uytXj8n5xvSqtBD2U1ZwIpnINSNpOtdKVnCpUYiYlIueWVMYFzx0JLBcIMyBZcTF_IRK1lSfFxd63j-F1pDSYbRijzyeN0KBnUmgNmSX2rPxsSpHWpo-uw_hugJvvpM130maXtNklbaoskntRymTfUPy1_kf1Bd0zhZA</recordid><startdate>20180101</startdate><enddate>20180101</enddate><creator>Parand, Kourosh</creator><creator>Latifi, Sobhan</creator><creator>Delkhosh, Mehdi</creator><creator>Moayeri, Mohammad M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>20180101</creationdate><title>Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium</title><author>Parand, Kourosh ; Latifi, Sobhan ; Delkhosh, Mehdi ; Moayeri, Mohammad M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-58ee163f1ae9c69495364a42733aa00ce4e9c204e9ae1c02a171e35028bee2dc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Accuracy</topic><topic>Algebra</topic><topic>Applied and Technical Physics</topic><topic>Approximation</topic><topic>Atomic</topic><topic>Boundary conditions</topic><topic>Collocation methods</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Decomposition</topic><topic>Differential equations</topic><topic>Engineering</topic><topic>Investigations</topic><topic>Mathematical and Computational Physics</topic><topic>Methods</topic><topic>Molecular</topic><topic>Numerical analysis</topic><topic>Optical and Plasma Physics</topic><topic>Ordinary differential equations</topic><topic>Partial differential equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Porous materials</topic><topic>Porous media</topic><topic>Regular Article</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Parand, Kourosh</creatorcontrib><creatorcontrib>Latifi, Sobhan</creatorcontrib><creatorcontrib>Delkhosh, Mehdi</creatorcontrib><creatorcontrib>Moayeri, Mohammad M.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>European physical journal plus</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Parand, Kourosh</au><au>Latifi, Sobhan</au><au>Delkhosh, Mehdi</au><au>Moayeri, Mohammad M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium</atitle><jtitle>European physical journal plus</jtitle><stitle>Eur. Phys. J. Plus</stitle><date>2018-01-01</date><risdate>2018</risdate><volume>133</volume><issue>1</issue><spage>28</spage><pages>28-</pages><artnum>28</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>.
In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval
[
0
,
∞
)
. Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope,
y
(
0
)
, is obtained as
-
1
.
191790649719421734122828603800159364
for
η
=
0
.
5
. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/i2018-11859-5</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2190-5444 |
| ispartof | European physical journal plus, 2018-01, Vol.133 (1), p.28, Article 28 |
| issn | 2190-5444 2190-5444 |
| language | eng |
| recordid | cdi_proquest_journals_2919732991 |
| source | Springer Nature |
| subjects | Accuracy Algebra Applied and Technical Physics Approximation Atomic Boundary conditions Collocation methods Complex Systems Condensed Matter Physics Decomposition Differential equations Engineering Investigations Mathematical and Computational Physics Methods Molecular Numerical analysis Optical and Plasma Physics Ordinary differential equations Partial differential equations Physics Physics and Astronomy Porous materials Porous media Regular Article Theoretical |
| title | Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-09T18%3A55%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Generalized%20Lagrangian%20Jacobi%20Gauss%20collocation%20method%20for%20solving%20unsteady%20isothermal%20gas%20through%20a%20micro-nano%20porous%20medium&rft.jtitle=European%20physical%20journal%20plus&rft.au=Parand,%20Kourosh&rft.date=2018-01-01&rft.volume=133&rft.issue=1&rft.spage=28&rft.pages=28-&rft.artnum=28&rft.issn=2190-5444&rft.eissn=2190-5444&rft_id=info:doi/10.1140/epjp/i2018-11859-5&rft_dat=%3Cproquest_cross%3E2919732991%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c319t-58ee163f1ae9c69495364a42733aa00ce4e9c204e9ae1c02a171e35028bee2dc3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2919732991&rft_id=info:pmid/&rfr_iscdi=true |