Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis

Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical me...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of Advances in Mathematics and Computer Science 2021-07, p.11-23
Hauptverfasser: Ihoeghian, N. A., John, B. O.
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 23
container_issue
container_start_page 11
container_title Journal of Advances in Mathematics and Computer Science
container_volume
creator Ihoeghian, N. A.
John, B. O.
description Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical methods with much difficulties. However, the great majority of ODEs, especially the non-linear ones and those that involve large sets of simultaneous differential equations, do not have analytical solutions but require the application of numerical techniques.  This work focused on exemplifying numerical approximations (Adams-Bashforth-Moulton, Bogacki-Shampine, Euler) of ODEs Initial value Problem in its simplest approach using a case study of gluconic acid frementation by Psuedonomas Ovalis. The performance of the methods was checked by comparing their accuracy.  The accuracy was detrermined by the size of the discretization error estimated from the difference between analytical solution and numerical approximations. The results obtained are in good agreement with the exact solution. This work affirms that numerical methods give approximate solutions with less rigorous work and time as there is room for flexibility in terms of using different step sizes with the Euler solver as most accurate.
doi_str_mv 10.9734/jamcs/2021/v36i630369
format Article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_9734_jamcs_2021_v36i630369</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_9734_jamcs_2021_v36i630369</sourcerecordid><originalsourceid>FETCH-crossref_primary_10_9734_jamcs_2021_v36i6303693</originalsourceid><addsrcrecordid>eNqdj9FKwzAUhoMoONweQTgvMJs2WWbxqszNeaODibchTVOIJE3Jacf69rZD0GuvzoHz_x_nI-Q-pQ_5mvHkS3mNSUazNDkxYQWjTORXZJbxlVjmuXi8_rPfkgWiLSnna86yTMzI-a33JlqtHBRtG8PZetXZ0CCEGt6ftwivje3seP5UrjdwiKF0xj9BARuFBo5dXw1T9sX1OjRWQ6FtBTsTvWm6CwrKAQ5o-ir40KgRfFLO4pzc1MqhWfzMO7LabT82-6WOATGaWrZx_CUOMqVyMpUXUzmZyl9T9t_eN-iZYak</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis</title><source>Alma/SFX Local Collection</source><creator>Ihoeghian, N. A. ; John, B. O.</creator><creatorcontrib>Ihoeghian, N. A. ; John, B. O.</creatorcontrib><description>Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical methods with much difficulties. However, the great majority of ODEs, especially the non-linear ones and those that involve large sets of simultaneous differential equations, do not have analytical solutions but require the application of numerical techniques.  This work focused on exemplifying numerical approximations (Adams-Bashforth-Moulton, Bogacki-Shampine, Euler) of ODEs Initial value Problem in its simplest approach using a case study of gluconic acid frementation by Psuedonomas Ovalis. The performance of the methods was checked by comparing their accuracy.  The accuracy was detrermined by the size of the discretization error estimated from the difference between analytical solution and numerical approximations. The results obtained are in good agreement with the exact solution. This work affirms that numerical methods give approximate solutions with less rigorous work and time as there is room for flexibility in terms of using different step sizes with the Euler solver as most accurate.</description><identifier>ISSN: 2456-9968</identifier><identifier>EISSN: 2456-9968</identifier><identifier>DOI: 10.9734/jamcs/2021/v36i630369</identifier><language>eng</language><ispartof>Journal of Advances in Mathematics and Computer Science, 2021-07, p.11-23</ispartof><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Ihoeghian, N. A.</creatorcontrib><creatorcontrib>John, B. O.</creatorcontrib><title>Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis</title><title>Journal of Advances in Mathematics and Computer Science</title><description>Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical methods with much difficulties. However, the great majority of ODEs, especially the non-linear ones and those that involve large sets of simultaneous differential equations, do not have analytical solutions but require the application of numerical techniques.  This work focused on exemplifying numerical approximations (Adams-Bashforth-Moulton, Bogacki-Shampine, Euler) of ODEs Initial value Problem in its simplest approach using a case study of gluconic acid frementation by Psuedonomas Ovalis. The performance of the methods was checked by comparing their accuracy.  The accuracy was detrermined by the size of the discretization error estimated from the difference between analytical solution and numerical approximations. The results obtained are in good agreement with the exact solution. This work affirms that numerical methods give approximate solutions with less rigorous work and time as there is room for flexibility in terms of using different step sizes with the Euler solver as most accurate.</description><issn>2456-9968</issn><issn>2456-9968</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNqdj9FKwzAUhoMoONweQTgvMJs2WWbxqszNeaODibchTVOIJE3Jacf69rZD0GuvzoHz_x_nI-Q-pQ_5mvHkS3mNSUazNDkxYQWjTORXZJbxlVjmuXi8_rPfkgWiLSnna86yTMzI-a33JlqtHBRtG8PZetXZ0CCEGt6ftwivje3seP5UrjdwiKF0xj9BARuFBo5dXw1T9sX1OjRWQ6FtBTsTvWm6CwrKAQ5o-ir40KgRfFLO4pzc1MqhWfzMO7LabT82-6WOATGaWrZx_CUOMqVyMpUXUzmZyl9T9t_eN-iZYak</recordid><startdate>20210714</startdate><enddate>20210714</enddate><creator>Ihoeghian, N. A.</creator><creator>John, B. O.</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210714</creationdate><title>Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis</title><author>Ihoeghian, N. A. ; John, B. O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-crossref_primary_10_9734_jamcs_2021_v36i6303693</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><toplevel>online_resources</toplevel><creatorcontrib>Ihoeghian, N. A.</creatorcontrib><creatorcontrib>John, B. O.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of Advances in Mathematics and Computer Science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ihoeghian, N. A.</au><au>John, B. O.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis</atitle><jtitle>Journal of Advances in Mathematics and Computer Science</jtitle><date>2021-07-14</date><risdate>2021</risdate><spage>11</spage><epage>23</epage><pages>11-23</pages><issn>2456-9968</issn><eissn>2456-9968</eissn><abstract>Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical methods with much difficulties. However, the great majority of ODEs, especially the non-linear ones and those that involve large sets of simultaneous differential equations, do not have analytical solutions but require the application of numerical techniques.  This work focused on exemplifying numerical approximations (Adams-Bashforth-Moulton, Bogacki-Shampine, Euler) of ODEs Initial value Problem in its simplest approach using a case study of gluconic acid frementation by Psuedonomas Ovalis. The performance of the methods was checked by comparing their accuracy.  The accuracy was detrermined by the size of the discretization error estimated from the difference between analytical solution and numerical approximations. The results obtained are in good agreement with the exact solution. This work affirms that numerical methods give approximate solutions with less rigorous work and time as there is room for flexibility in terms of using different step sizes with the Euler solver as most accurate.</abstract><doi>10.9734/jamcs/2021/v36i630369</doi></addata></record>
fulltext fulltext
identifier ISSN: 2456-9968
ispartof Journal of Advances in Mathematics and Computer Science, 2021-07, p.11-23
issn 2456-9968
2456-9968
language eng
recordid cdi_crossref_primary_10_9734_jamcs_2021_v36i630369
source Alma/SFX Local Collection
title Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T09%3A58%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Numerical%20Approximations%20of%20ODEs%20Initial%20Value%20Problem;%20A%20Case%20Study%20of%20Gluconic%20Acid%20Fermentation%20by%20Pseudomonas%20ovalis&rft.jtitle=Journal%20of%20Advances%20in%20Mathematics%20and%20Computer%20Science&rft.au=Ihoeghian,%20N.%20A.&rft.date=2021-07-14&rft.spage=11&rft.epage=23&rft.pages=11-23&rft.issn=2456-9968&rft.eissn=2456-9968&rft_id=info:doi/10.9734/jamcs/2021/v36i630369&rft_dat=%3Ccrossref%3E10_9734_jamcs_2021_v36i630369%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true