On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method

On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method

We study higher-order boundary value problems (HOBVP) for higher-order nonlinear differential equation. We make comparison among differential transformation method (DTM), Adomian decomposition method (ADM), and exact solutions. We provide several examples in order to compare our results. We extend a...

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Main Authors: Che Haziqah Che Hussin, Adem Kiliçman
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2011/724927
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spelling doaj-8010678a64124c5995a10ea8db53ba4c2020-11-24T22:50:34ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472011-01-01201110.1155/2011/724927724927On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition MethodChe Haziqah Che Hussin0Adem Kiliçman1Department of Mathematics, University Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaDepartment of Mathematics, University Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaWe study higher-order boundary value problems (HOBVP) for higher-order nonlinear differential equation. We make comparison among differential transformation method (DTM), Adomian decomposition method (ADM), and exact solutions. We provide several examples in order to compare our results. We extend and prove a theorem for nonlinear differential equations by using the DTM. The numerical examples show that the DTM is a good method compared to the ADM since it is effective, uses less time in computation, easy to implement and achieve high accuracy. In addition, DTM has many advantages compared to ADM since the calculation of Adomian polynomial is tedious. From the numerical results, DTM is suitable to apply for nonlinear problems.http://dx.doi.org/10.1155/2011/724927
collection DOAJ
language English
format Article
sources DOAJ
author Che Haziqah Che Hussin
Adem Kiliçman
spellingShingle Che Haziqah Che Hussin
Adem Kiliçman
On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method
Mathematical Problems in Engineering
author_facet Che Haziqah Che Hussin
Adem Kiliçman
author_sort Che Haziqah Che Hussin
title On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method
title_short On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method
title_full On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method
title_fullStr On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method
title_full_unstemmed On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method
title_sort on the solutions of nonlinear higher-order boundary value problems by using differential transformation method and adomian decomposition method
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2011-01-01
description We study higher-order boundary value problems (HOBVP) for higher-order nonlinear differential equation. We make comparison among differential transformation method (DTM), Adomian decomposition method (ADM), and exact solutions. We provide several examples in order to compare our results. We extend and prove a theorem for nonlinear differential equations by using the DTM. The numerical examples show that the DTM is a good method compared to the ADM since it is effective, uses less time in computation, easy to implement and achieve high accuracy. In addition, DTM has many advantages compared to ADM since the calculation of Adomian polynomial is tedious. From the numerical results, DTM is suitable to apply for nonlinear problems.
url http://dx.doi.org/10.1155/2011/724927
work_keys_str_mv AT chehaziqahchehussin onthesolutionsofnonlinearhigherorderboundaryvalueproblemsbyusingdifferentialtransformationmethodandadomiandecompositionmethod
AT ademkilicman onthesolutionsofnonlinearhigherorderboundaryvalueproblemsbyusingdifferentialtransformationmethodandadomiandecompositionmethod
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