Numerical solutions of volterra integro-differential equations using general linear method

Faranak Rabiei; Fatin Abd Hamid; Zanariah Abd Majid; Fudziah Ismail

doi:10.3934/naco.2019042

Numerical solutions of volterra integro-differential equations using general linear method

Faranak Rabiei
, Fatin Abd Hamid
, Zanariah Abd Majid
, Fudziah Ismail

Malaysia School of Engineering

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

In this paper, a third order General Linear Method for finding the numerical solution of Volterra integro-differential equation is considered. The order conditions of the proposed method are derived based on techniques of B-series and rooted trees. The integral operator in Volterra integro-differential equation approximated using Simpsons rule and Lagrange interpolation is discussed. To illustrate the efficiency of third order General Linear Method, we compare the method with a third order Runge-Kutta method.

Original language	English
Pages (from-to)	433-444
Number of pages	12
Journal	Numerical Algebra, Control and Optimization
Volume	9
Issue number	4
DOIs	https://doi.org/10.3934/naco.2019042
Publication status	Published - Dec 2019

Keywords

And phrases
General linear method
Quadrature rule
Third order method
Volterra integro-differential equations

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346338557-oaFinal published version, 506 KBLicence: CC BY

Cite this

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title = "Numerical solutions of volterra integro-differential equations using general linear method",

abstract = "In this paper, a third order General Linear Method for finding the numerical solution of Volterra integro-differential equation is considered. The order conditions of the proposed method are derived based on techniques of B-series and rooted trees. The integral operator in Volterra integro-differential equation approximated using Simpsons rule and Lagrange interpolation is discussed. To illustrate the efficiency of third order General Linear Method, we compare the method with a third order Runge-Kutta method.",

keywords = "And phrases, General linear method, Quadrature rule, Third order method, Volterra integro-differential equations",

author = "Faranak Rabiei and Hamid, \{Fatin Abd\} and Majid, \{Zanariah Abd\} and Fudziah Ismail",

note = "Funding Information: 6. Acknowledgments. This work was part of FRGS research grant project (Ref: FRGS/2/2013/SG04/UPM/02/1, vote number 5524421 ) and the authors wish to thank on Ministry of Higher Education Malaysia for supporting this research. Publisher Copyright: {\textcopyright} 2019, American Institute of Mathematical Sciences. All rights reserved. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

year = "2019",

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doi = "10.3934/naco.2019042",

language = "English",

volume = "9",

pages = "433--444",

journal = "Numerical Algebra, Control and Optimization",

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AU - Rabiei, Faranak

AU - Hamid, Fatin Abd

AU - Majid, Zanariah Abd

AU - Ismail, Fudziah

N1 - Funding Information: 6. Acknowledgments. This work was part of FRGS research grant project (Ref: FRGS/2/2013/SG04/UPM/02/1, vote number 5524421 ) and the authors wish to thank on Ministry of Higher Education Malaysia for supporting this research. Publisher Copyright: © 2019, American Institute of Mathematical Sciences. All rights reserved. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/12

Y1 - 2019/12

N2 - In this paper, a third order General Linear Method for finding the numerical solution of Volterra integro-differential equation is considered. The order conditions of the proposed method are derived based on techniques of B-series and rooted trees. The integral operator in Volterra integro-differential equation approximated using Simpsons rule and Lagrange interpolation is discussed. To illustrate the efficiency of third order General Linear Method, we compare the method with a third order Runge-Kutta method.

AB - In this paper, a third order General Linear Method for finding the numerical solution of Volterra integro-differential equation is considered. The order conditions of the proposed method are derived based on techniques of B-series and rooted trees. The integral operator in Volterra integro-differential equation approximated using Simpsons rule and Lagrange interpolation is discussed. To illustrate the efficiency of third order General Linear Method, we compare the method with a third order Runge-Kutta method.

KW - And phrases

KW - General linear method

KW - Quadrature rule

KW - Third order method

KW - Volterra integro-differential equations

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DO - 10.3934/naco.2019042

M3 - Article

AN - SCOPUS:85076892087

SN - 2155-3289

VL - 9

SP - 433

EP - 444

JO - Numerical Algebra, Control and Optimization

JF - Numerical Algebra, Control and Optimization

IS - 4

ER -

Numerical solutions of volterra integro-differential equations using general linear method

Abstract

Keywords

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