Numerical solution for application problems by third order 1-point block backward differentiation formula with off-step point

Amiratul Ashikin Nasarudin; Zarina Bibi Ibrahim; Nor Ain Azeany Mohd Nasir

Numerical solution for application problems by third order 1-point block backward differentiation formula with off-step point

Amiratul Ashikin Nasarudin, Zarina Bibi Ibrahim^*, Nor Ain Azeany Mohd Nasir

^*Corresponding author for this work

School of Mathematical & Computer Sciences

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

Abstract

This paper aims to develop an extended Third Order 1-point Block Backward Differentiation Formula with Off-Step Point (BBDFO(3)). The method is derived by Lagrange Interpolation using two back values and one off-step point. A BBDFO(3) method is capable to become an alternative solver in solving applied problems of ODEs by implementing Newton’s iteration method. Several application problems are solved in this study such as free falling problem, mixing problem and electrical circuit problem. The performance of the numerical results show that method BBDFO(3) produced better accuracy as compared with other existing methods.

Original language	English
Pages (from-to)	221-227
Number of pages	7
Journal	Journal of Advanced Research in Dynamical and Control Systems
Volume	11
Issue number	12 Special Issue
Publication status	Published - 2019

Keywords

Application problem
Backward differentiation formula
Off-step point
Ordinary differential equation

ASJC Scopus subject areas

General Computer Science
General Engineering

Cite this

@article{9617fe10f7d64564a79aab828f5e0701,

title = "Numerical solution for application problems by third order 1-point block backward differentiation formula with off-step point",

abstract = "This paper aims to develop an extended Third Order 1-point Block Backward Differentiation Formula with Off-Step Point (BBDFO(3)). The method is derived by Lagrange Interpolation using two back values and one off-step point. A BBDFO(3) method is capable to become an alternative solver in solving applied problems of ODEs by implementing Newton{\textquoteright}s iteration method. Several application problems are solved in this study such as free falling problem, mixing problem and electrical circuit problem. The performance of the numerical results show that method BBDFO(3) produced better accuracy as compared with other existing methods.",

keywords = "Application problem, Backward differentiation formula, Off-step point, Ordinary differential equation",

author = "Nasarudin, {Amiratul Ashikin} and Ibrahim, {Zarina Bibi} and {Mohd Nasir}, {Nor Ain Azeany}",

note = "Funding Information: This research is funded by Institute for Mathematical Research, Universiti Putra Malaysia under research grant GP-IPS/2018/9624600. Publisher Copyright: {\textcopyright} Institute of Advanced Scientific Research, Inc.. All rights reserved.",

year = "2019",

language = "English",

volume = "11",

pages = "221--227",

journal = "Journal of Advanced Research in Dynamical and Control Systems",

issn = "1943-023X",

publisher = "Institute of Advanced Scientific Research",

number = "12 Special Issue",

}

Numerical solution for application problems by third order 1-point block backward differentiation formula with off-step point. / Nasarudin, Amiratul Ashikin; Ibrahim, Zarina Bibi; Mohd Nasir, Nor Ain Azeany.
In: Journal of Advanced Research in Dynamical and Control Systems, Vol. 11, No. 12 Special Issue, 2019, p. 221-227.

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

TY - JOUR

T1 - Numerical solution for application problems by third order 1-point block backward differentiation formula with off-step point

AU - Nasarudin, Amiratul Ashikin

AU - Ibrahim, Zarina Bibi

AU - Mohd Nasir, Nor Ain Azeany

N1 - Funding Information: This research is funded by Institute for Mathematical Research, Universiti Putra Malaysia under research grant GP-IPS/2018/9624600. Publisher Copyright: © Institute of Advanced Scientific Research, Inc.. All rights reserved.

PY - 2019

Y1 - 2019

N2 - This paper aims to develop an extended Third Order 1-point Block Backward Differentiation Formula with Off-Step Point (BBDFO(3)). The method is derived by Lagrange Interpolation using two back values and one off-step point. A BBDFO(3) method is capable to become an alternative solver in solving applied problems of ODEs by implementing Newton’s iteration method. Several application problems are solved in this study such as free falling problem, mixing problem and electrical circuit problem. The performance of the numerical results show that method BBDFO(3) produced better accuracy as compared with other existing methods.

AB - This paper aims to develop an extended Third Order 1-point Block Backward Differentiation Formula with Off-Step Point (BBDFO(3)). The method is derived by Lagrange Interpolation using two back values and one off-step point. A BBDFO(3) method is capable to become an alternative solver in solving applied problems of ODEs by implementing Newton’s iteration method. Several application problems are solved in this study such as free falling problem, mixing problem and electrical circuit problem. The performance of the numerical results show that method BBDFO(3) produced better accuracy as compared with other existing methods.

KW - Application problem

KW - Backward differentiation formula

KW - Off-step point

KW - Ordinary differential equation

UR - http://www.scopus.com/inward/record.url?scp=85077885738&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85077885738

SN - 1943-023X

VL - 11

SP - 221

EP - 227

JO - Journal of Advanced Research in Dynamical and Control Systems

JF - Journal of Advanced Research in Dynamical and Control Systems

IS - 12 Special Issue

ER -

Numerical solution for application problems by third order 1-point block backward differentiation formula with off-step point

Abstract

Keywords

ASJC Scopus subject areas

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