A Recursive Method for Calculation of Collocation Constants in Orthogonal Collocation Method

Takahiro Hasegawa, Fumihide Shiraishi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

An efficient method for calculation of collocation constants in the orthogonal collocation method was discussed. To make it possible to calculate the collocation constants of arbitrary order using the same subroutine, an algorithm utilizing their recursive properties was proposed. The first and second-order collocation constants calculated based on the algorithm were confirmed to have the same high accuracies as those by the method previously reported. From the result of investigation on accuracies of the approximate values to high-order derivatives of a trigonometric function, the proposed algorithm was shown to also be useful in the calculation of higher-order collocation constants. The execution time required to calculate a set of collocation constants was almost the same as that of the previous method.

Original languageEnglish
Pages (from-to)1373-1378
Number of pages6
Journalkagaku kogaku ronbunshu
Volume22
Issue number6
DOIs
Publication statusPublished - Jan 1 1996
Externally publishedYes

Fingerprint

Subroutines
Derivatives

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Chemical Engineering(all)

Cite this

A Recursive Method for Calculation of Collocation Constants in Orthogonal Collocation Method. / Hasegawa, Takahiro; Shiraishi, Fumihide.

In: kagaku kogaku ronbunshu, Vol. 22, No. 6, 01.01.1996, p. 1373-1378.

Research output: Contribution to journalArticle

@article{6861d99e77f542fe87c144260dc167f5,
title = "A Recursive Method for Calculation of Collocation Constants in Orthogonal Collocation Method",
abstract = "An efficient method for calculation of collocation constants in the orthogonal collocation method was discussed. To make it possible to calculate the collocation constants of arbitrary order using the same subroutine, an algorithm utilizing their recursive properties was proposed. The first and second-order collocation constants calculated based on the algorithm were confirmed to have the same high accuracies as those by the method previously reported. From the result of investigation on accuracies of the approximate values to high-order derivatives of a trigonometric function, the proposed algorithm was shown to also be useful in the calculation of higher-order collocation constants. The execution time required to calculate a set of collocation constants was almost the same as that of the previous method.",
author = "Takahiro Hasegawa and Fumihide Shiraishi",
year = "1996",
month = "1",
day = "1",
doi = "10.1252/kakoronbunshu.22.1373",
language = "English",
volume = "22",
pages = "1373--1378",
journal = "Kagaku Kogaku Ronbunshu",
issn = "0386-216X",
publisher = "The Society of Chemical Engineers, Japan",
number = "6",

}

TY - JOUR

T1 - A Recursive Method for Calculation of Collocation Constants in Orthogonal Collocation Method

AU - Hasegawa, Takahiro

AU - Shiraishi, Fumihide

PY - 1996/1/1

Y1 - 1996/1/1

N2 - An efficient method for calculation of collocation constants in the orthogonal collocation method was discussed. To make it possible to calculate the collocation constants of arbitrary order using the same subroutine, an algorithm utilizing their recursive properties was proposed. The first and second-order collocation constants calculated based on the algorithm were confirmed to have the same high accuracies as those by the method previously reported. From the result of investigation on accuracies of the approximate values to high-order derivatives of a trigonometric function, the proposed algorithm was shown to also be useful in the calculation of higher-order collocation constants. The execution time required to calculate a set of collocation constants was almost the same as that of the previous method.

AB - An efficient method for calculation of collocation constants in the orthogonal collocation method was discussed. To make it possible to calculate the collocation constants of arbitrary order using the same subroutine, an algorithm utilizing their recursive properties was proposed. The first and second-order collocation constants calculated based on the algorithm were confirmed to have the same high accuracies as those by the method previously reported. From the result of investigation on accuracies of the approximate values to high-order derivatives of a trigonometric function, the proposed algorithm was shown to also be useful in the calculation of higher-order collocation constants. The execution time required to calculate a set of collocation constants was almost the same as that of the previous method.

UR - http://www.scopus.com/inward/record.url?scp=21444450094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21444450094&partnerID=8YFLogxK

U2 - 10.1252/kakoronbunshu.22.1373

DO - 10.1252/kakoronbunshu.22.1373

M3 - Article

AN - SCOPUS:21444450094

VL - 22

SP - 1373

EP - 1378

JO - Kagaku Kogaku Ronbunshu

JF - Kagaku Kogaku Ronbunshu

SN - 0386-216X

IS - 6

ER -