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Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations

In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solutio...

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Main Authors: Che Haziqah Che Hussin, Arif Mandangan, Adem Kilicman, Muhamad Azlan Daud, Nurliyana Juhan
Format: Article
Language:English
English
Published: ResearchGate 2016
Subjects:
QA Mathematics
QA150-272.5 Algebra
Online Access:https://eprints.ums.edu.my/id/eprint/21443/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/21443/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/21443/
http://dx.doi.org/10.11113/jt.v78.8969
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spelling my.ums.eprints.214432024-01-25T08:00:20Z https://eprints.ums.edu.my/id/eprint/21443/ Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations Che Haziqah Che Hussin Arif Mandangan Adem Kilicman Muhamad Azlan Daud Nurliyana Juhan QA Mathematics QA150-272.5 Algebra In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solution. Absolute relative error (ARE) for each iteration can be computed. Therefore, the maximum absolute relative error (MARE) of the DTM can be obtained. To show that the solution given by the DTM has higher level of accuracy, the absolute relative error of the DTM has been compared with the other methods such as Adomian decomposition method with Green’s function, modified decomposition method (MDM), homotopy perturbation method (HPM), Variational Iteration Method (VIM) and Quintic B-Spline Collocation Method. Comparison graphs are given at the end of this paper. The obtained result shows that the proposed method is able to provide better approximation in term of accuracy. ResearchGate 2016 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/21443/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/21443/2/FULL%20TEXT.pdf Che Haziqah Che Hussin and Arif Mandangan and Adem Kilicman and Muhamad Azlan Daud and Nurliyana Juhan (2016) Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations. Jurnal Teknologi, 78 (6-4). pp. 13-19. doi.org/10.11113/jt.v78.8969 http://dx.doi.org/10.11113/jt.v78.8969
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
English
topic QA Mathematics
QA150-272.5 Algebra
spellingShingle QA Mathematics
QA150-272.5 Algebra
Che Haziqah Che Hussin
Arif Mandangan
Adem Kilicman
Muhamad Azlan Daud
Nurliyana Juhan
Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations
description In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solution. Absolute relative error (ARE) for each iteration can be computed. Therefore, the maximum absolute relative error (MARE) of the DTM can be obtained. To show that the solution given by the DTM has higher level of accuracy, the absolute relative error of the DTM has been compared with the other methods such as Adomian decomposition method with Green’s function, modified decomposition method (MDM), homotopy perturbation method (HPM), Variational Iteration Method (VIM) and Quintic B-Spline Collocation Method. Comparison graphs are given at the end of this paper. The obtained result shows that the proposed method is able to provide better approximation in term of accuracy.
format Article
author Che Haziqah Che Hussin
Arif Mandangan
Adem Kilicman
Muhamad Azlan Daud
Nurliyana Juhan
author_facet Che Haziqah Che Hussin
Arif Mandangan
Adem Kilicman
Muhamad Azlan Daud
Nurliyana Juhan
author_sort Che Haziqah Che Hussin
title Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations
title_short Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations
title_full Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations
title_fullStr Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations
title_full_unstemmed Differential Transformation Method for Solving Sixth-Order Boundary Value Problems of Ordinary Differential Equations
title_sort differential transformation method for solving sixth-order boundary value problems of ordinary differential equations
publisher ResearchGate
publishDate 2016
url https://eprints.ums.edu.my/id/eprint/21443/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/21443/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/21443/
http://dx.doi.org/10.11113/jt.v78.8969
_version_ 1789425983486427136
score 13.251813

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