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

Che Haziqah Che Hussin | Zendy; Adem Kılıçman | Zendy

Open Access

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

Author(s) -

Che Haziqah Che Hussin,

Adem Kılıçman

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/724927

Subject(s) - adomian decomposition method , transformation (genetics) , mathematics , nonlinear system , boundary value problem , decomposition , mathematical analysis , order (exchange) , decomposition method (queueing theory) , differential (mechanical device) , differential equation , physics , statistics , economics , thermodynamics , gene , biochemistry , chemistry , finance , quantum mechanics , ecology , biology

We study higher-order boundary value problems(HOBVP) for higher-order nonlinear differential equation. We make comparisonamong differential transformation method (DTM), Adomian decompositionmethod (ADM), and exact solutions. We provide several examples inorder to compare our results. We extend and prove a theorem for nonlineardifferential equations by using the DTM. The numerical examples showthat 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. Inaddition, DTM has many advantages compared to ADM since the calculation ofAdomian polynomial is tedious. From the numerical results, DTM is suitableto apply for nonlinear problems

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