Separate multinode ascending derivatives expansion (Demiralp's SMADE): Basis polynomials

Burcu Tunga

doi:10.1063/1.4938946

Separate multinode ascending derivatives expansion (Demiralp's SMADE): Basis polynomials

Burcu Tunga^*

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

Separate Multinode Ascending Derivatives Expansion (SMADE) is a recently developed function representation method based on "Separate Node Ascending Derivatives Expansion (SNADE)" which was proposed by Prof. Demiralp. For this reason we call this method in this work "Demiralp's SMADE". The basic difference between two methods is that SNADE uses one separate node for each derivative to construct the expansion while SMADE uses multinodes for the same entities even though the separate nature of the nodes is not mandatory. This study focuses on SMADE both to present all important details of the method including its formulation and its basis polynomials.

Original language	English
Title of host publication	International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015
Editors	Zacharoula Kalogiratou, Theodore E. Simos, Theodore Monovasilis, Theodore E. Simos, Theodore E. Simos
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735413498
DOIs	https://doi.org/10.1063/1.4938946
Publication status	Published - 31 Dec 2015
Event	International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015 - Athens, Greece Duration: 20 Mar 2015 → 23 Mar 2015

Publication series

Name	AIP Conference Proceedings
Volume	1702
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015
Country/Territory	Greece
City	Athens
Period	20/03/15 → 23/03/15

Bibliographical note

Publisher Copyright:
© 2015 AIP Publishing LLC.

Keywords

Polynomial recursions
Remainder bounds
SMADE Convergence
SMADE expansion
SNADE
Univariate functions

Access to Document

10.1063/1.4938946

Cite this

Tunga, B. (2015). Separate multinode ascending derivatives expansion (Demiralp's SMADE): Basis polynomials. In Z. Kalogiratou, T. E. Simos, T. Monovasilis, T. E. Simos, & T. E. Simos (Eds.), International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015 Article 170011 (AIP Conference Proceedings; Vol. 1702). American Institute of Physics Inc.. https://doi.org/10.1063/1.4938946

Tunga, Burcu. / Separate multinode ascending derivatives expansion (Demiralp's SMADE) : Basis polynomials. International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015. editor / Zacharoula Kalogiratou ; Theodore E. Simos ; Theodore Monovasilis ; Theodore E. Simos ; Theodore E. Simos. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

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abstract = "Separate Multinode Ascending Derivatives Expansion (SMADE) is a recently developed function representation method based on {"}Separate Node Ascending Derivatives Expansion (SNADE){"} which was proposed by Prof. Demiralp. For this reason we call this method in this work {"}Demiralp's SMADE{"}. The basic difference between two methods is that SNADE uses one separate node for each derivative to construct the expansion while SMADE uses multinodes for the same entities even though the separate nature of the nodes is not mandatory. This study focuses on SMADE both to present all important details of the method including its formulation and its basis polynomials.",

keywords = "Polynomial recursions, Remainder bounds, SMADE Convergence, SMADE expansion, SNADE, Univariate functions",

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note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015 ; Conference date: 20-03-2015 Through 23-03-2015",

year = "2015",

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Tunga, B 2015, Separate multinode ascending derivatives expansion (Demiralp's SMADE): Basis polynomials. in Z Kalogiratou, TE Simos, T Monovasilis, TE Simos & TE Simos (eds), International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015., 170011, AIP Conference Proceedings, vol. 1702, American Institute of Physics Inc., International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015, Athens, Greece, 20/03/15. https://doi.org/10.1063/1.4938946

Separate multinode ascending derivatives expansion (Demiralp's SMADE): Basis polynomials. / Tunga, Burcu.
International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015. ed. / Zacharoula Kalogiratou; Theodore E. Simos; Theodore Monovasilis; Theodore E. Simos; Theodore E. Simos. American Institute of Physics Inc., 2015. 170011 (AIP Conference Proceedings; Vol. 1702).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Separate Multinode Ascending Derivatives Expansion (SMADE) is a recently developed function representation method based on "Separate Node Ascending Derivatives Expansion (SNADE)" which was proposed by Prof. Demiralp. For this reason we call this method in this work "Demiralp's SMADE". The basic difference between two methods is that SNADE uses one separate node for each derivative to construct the expansion while SMADE uses multinodes for the same entities even though the separate nature of the nodes is not mandatory. This study focuses on SMADE both to present all important details of the method including its formulation and its basis polynomials.

AB - Separate Multinode Ascending Derivatives Expansion (SMADE) is a recently developed function representation method based on "Separate Node Ascending Derivatives Expansion (SNADE)" which was proposed by Prof. Demiralp. For this reason we call this method in this work "Demiralp's SMADE". The basic difference between two methods is that SNADE uses one separate node for each derivative to construct the expansion while SMADE uses multinodes for the same entities even though the separate nature of the nodes is not mandatory. This study focuses on SMADE both to present all important details of the method including its formulation and its basis polynomials.

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KW - Remainder bounds

KW - SMADE Convergence

KW - SMADE expansion

KW - SNADE

KW - Univariate functions

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BT - International Conference of Computational Methods in Sciences and Engineering 2015, ICCMSE 2015

A2 - Kalogiratou, Zacharoula

A2 - Simos, Theodore E.

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PB - American Institute of Physics Inc.

Y2 - 20 March 2015 through 23 March 2015

ER -

Separate multinode ascending derivatives expansion (Demiralp's SMADE): Basis polynomials

Abstract

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Bibliographical note

Keywords

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