An efficient method for solving two-point boundary value problems with extremely high accuracy

Fumihide Shiraishi, Satoshi Fujiwara

研究成果: ジャーナルへの寄稿記事

11 引用 (Scopus)

抄録

A novel numerical method for solving two-point boundary value problems is presented. This method utilizes a recasting technique for transformation of fundamental differential equations into S-system (synergistic and saturable system) canonical form that consists of a set of simultaneous first-order differential equations, an efficient computational algorithm that was proposed to numerically solve the S-system differential equations, and the shooting method. A two-point boundary value problem associated with an immobilized enzyme reaction was investigated as a model system, and it was found that the accuracy of numerical solutions obtained by the proposed method was almost the same as the accuracy of the computer. Another advantage of the proposed method is that it enables one to write a generalized computer program for two-point boundary value problems. With such a program, the user can solve different types of two-point boundary value problems by just imputing S-system parameters that are obtained by recasting their fundamental differential equations.

元の言語英語
ページ(範囲)88-94
ページ数7
ジャーナルJOURNAL OF CHEMICAL ENGINEERING OF JAPAN
29
発行部数1
DOI
出版物ステータス出版済み - 2 1996
外部発表Yes

Fingerprint

Boundary value problems
Differential equations
Immobilized Enzymes
Computer program listings
Numerical methods
Enzymes

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Chemical Engineering(all)

これを引用

An efficient method for solving two-point boundary value problems with extremely high accuracy. / Shiraishi, Fumihide; Fujiwara, Satoshi.

:: JOURNAL OF CHEMICAL ENGINEERING OF JAPAN, 巻 29, 番号 1, 02.1996, p. 88-94.

研究成果: ジャーナルへの寄稿記事

@article{e5ae218e6a334da59b5299ac44161eec,
title = "An efficient method for solving two-point boundary value problems with extremely high accuracy",
abstract = "A novel numerical method for solving two-point boundary value problems is presented. This method utilizes a recasting technique for transformation of fundamental differential equations into S-system (synergistic and saturable system) canonical form that consists of a set of simultaneous first-order differential equations, an efficient computational algorithm that was proposed to numerically solve the S-system differential equations, and the shooting method. A two-point boundary value problem associated with an immobilized enzyme reaction was investigated as a model system, and it was found that the accuracy of numerical solutions obtained by the proposed method was almost the same as the accuracy of the computer. Another advantage of the proposed method is that it enables one to write a generalized computer program for two-point boundary value problems. With such a program, the user can solve different types of two-point boundary value problems by just imputing S-system parameters that are obtained by recasting their fundamental differential equations.",
author = "Fumihide Shiraishi and Satoshi Fujiwara",
year = "1996",
month = "2",
doi = "10.1252/jcej.29.88",
language = "English",
volume = "29",
pages = "88--94",
journal = "Journal of Chemical Engineering of Japan",
issn = "0021-9592",
publisher = "Society of Chemical Engineers, Japan",
number = "1",

}

TY - JOUR

T1 - An efficient method for solving two-point boundary value problems with extremely high accuracy

AU - Shiraishi, Fumihide

AU - Fujiwara, Satoshi

PY - 1996/2

Y1 - 1996/2

N2 - A novel numerical method for solving two-point boundary value problems is presented. This method utilizes a recasting technique for transformation of fundamental differential equations into S-system (synergistic and saturable system) canonical form that consists of a set of simultaneous first-order differential equations, an efficient computational algorithm that was proposed to numerically solve the S-system differential equations, and the shooting method. A two-point boundary value problem associated with an immobilized enzyme reaction was investigated as a model system, and it was found that the accuracy of numerical solutions obtained by the proposed method was almost the same as the accuracy of the computer. Another advantage of the proposed method is that it enables one to write a generalized computer program for two-point boundary value problems. With such a program, the user can solve different types of two-point boundary value problems by just imputing S-system parameters that are obtained by recasting their fundamental differential equations.

AB - A novel numerical method for solving two-point boundary value problems is presented. This method utilizes a recasting technique for transformation of fundamental differential equations into S-system (synergistic and saturable system) canonical form that consists of a set of simultaneous first-order differential equations, an efficient computational algorithm that was proposed to numerically solve the S-system differential equations, and the shooting method. A two-point boundary value problem associated with an immobilized enzyme reaction was investigated as a model system, and it was found that the accuracy of numerical solutions obtained by the proposed method was almost the same as the accuracy of the computer. Another advantage of the proposed method is that it enables one to write a generalized computer program for two-point boundary value problems. With such a program, the user can solve different types of two-point boundary value problems by just imputing S-system parameters that are obtained by recasting their fundamental differential equations.

UR - http://www.scopus.com/inward/record.url?scp=0029676356&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029676356&partnerID=8YFLogxK

U2 - 10.1252/jcej.29.88

DO - 10.1252/jcej.29.88

M3 - Article

AN - SCOPUS:0029676356

VL - 29

SP - 88

EP - 94

JO - Journal of Chemical Engineering of Japan

JF - Journal of Chemical Engineering of Japan

SN - 0021-9592

IS - 1

ER -