Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method

Necdet Bildik; Ali Konuralp; Funda Orakçi Bek; Semih Küçükarslan

doi:10.1016/j.amc.2005.02.037

Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method

Necdet Bildik^*, Ali Konuralp, Funda Orakçi Bek, Semih Küçükarslan

^*Corresponding author for this work

Manisa Celal Bayar University

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

79 Citations (Scopus)

Abstract

In this paper, the definitions and operations of the differential transform method [J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huarjung University Press, Wuuhahn, China, 1986] and Adomian's decomposition method which is given by George Adomian for approximate solution of linear and non-linear differential equations are expressed [G. Adomian, Convergent series solution of nonlinear equation, Comput. Appl. Math. 11 (1984) 113-117]. Different partial differential equations are solved under the view of these methods and compared with the approximate solution and analytic solution. At the end, these solutions are illustrated by tables and figures.

Original language	English
Pages (from-to)	551-567
Number of pages	17
Journal	Applied Mathematics and Computation
Volume	172
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2005.02.037
Publication status	Published - 1 Jan 2006
Externally published	Yes

Keywords

Decomposition method
Differential transform method
Initial value problem
Partial differential equation

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10.1016/j.amc.2005.02.037

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abstract = "In this paper, the definitions and operations of the differential transform method [J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huarjung University Press, Wuuhahn, China, 1986] and Adomian's decomposition method which is given by George Adomian for approximate solution of linear and non-linear differential equations are expressed [G. Adomian, Convergent series solution of nonlinear equation, Comput. Appl. Math. 11 (1984) 113-117]. Different partial differential equations are solved under the view of these methods and compared with the approximate solution and analytic solution. At the end, these solutions are illustrated by tables and figures.",

keywords = "Decomposition method, Differential transform method, Initial value problem, Partial differential equation",

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AU - Bildik, Necdet

AU - Konuralp, Ali

AU - Bek, Funda Orakçi

AU - Küçükarslan, Semih

PY - 2006/1/1

Y1 - 2006/1/1

N2 - In this paper, the definitions and operations of the differential transform method [J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huarjung University Press, Wuuhahn, China, 1986] and Adomian's decomposition method which is given by George Adomian for approximate solution of linear and non-linear differential equations are expressed [G. Adomian, Convergent series solution of nonlinear equation, Comput. Appl. Math. 11 (1984) 113-117]. Different partial differential equations are solved under the view of these methods and compared with the approximate solution and analytic solution. At the end, these solutions are illustrated by tables and figures.

AB - In this paper, the definitions and operations of the differential transform method [J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huarjung University Press, Wuuhahn, China, 1986] and Adomian's decomposition method which is given by George Adomian for approximate solution of linear and non-linear differential equations are expressed [G. Adomian, Convergent series solution of nonlinear equation, Comput. Appl. Math. 11 (1984) 113-117]. Different partial differential equations are solved under the view of these methods and compared with the approximate solution and analytic solution. At the end, these solutions are illustrated by tables and figures.

KW - Decomposition method

KW - Differential transform method

KW - Initial value problem

KW - Partial differential equation

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SN - 0096-3003

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EP - 567

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method

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Keywords

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