Direct solutions of N-th order initial value problems in decomposition series

F. Yahaya; I. Hashim; E. S. Ismail; A. K. Zulkifle

doi:10.1515/IJNSNS.2007.8.3.385

Direct solutions of N-th order initial value problems in decomposition series

F. Yahaya
, I. Hashim
, E. S. Ismail
, A. K. Zulkifle

Universiti Kebangsaan Malaysia
Universiti Tenaga Nasional

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

8 Scopus citations

Abstract

In this paper, a class of linear and non-linear ⁿth-order initial value problems (IVPs) is considered. The solutions of these IVPs are obtained by adapting the modified Adomian decomposition method (MADM) as an algorithm for approximating the solutions of the equations in a sequence of time intervals (i.e. time steps). In this way the series solutions are valid for quite a long time span. Several test cases are chosen to demonstrate the performance of the multistage modified Adomian decomposition method (MMADM).

Original language	English
Pages (from-to)	385-392
Number of pages	8
Journal	International Journal of Nonlinear Sciences and Numerical Simulation
Volume	8
Issue number	3
DOIs	https://doi.org/10.1515/IJNSNS.2007.8.3.385
State	Published - 2007
Externally published	Yes

Keywords

Adomian decomposition method
Initial value problems
Series solution

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10.1515/IJNSNS.2007.8.3.385

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title = "Direct solutions of N-th order initial value problems in decomposition series",

abstract = "In this paper, a class of linear and non-linear nth-order initial value problems (IVPs) is considered. The solutions of these IVPs are obtained by adapting the modified Adomian decomposition method (MADM) as an algorithm for approximating the solutions of the equations in a sequence of time intervals (i.e. time steps). In this way the series solutions are valid for quite a long time span. Several test cases are chosen to demonstrate the performance of the multistage modified Adomian decomposition method (MMADM).",

keywords = "Adomian decomposition method, Initial value problems, Series solution",

author = "F. Yahaya and I. Hashim and Ismail, \{E. S.\} and Zulkifle, \{A. K.\}",

year = "2007",

doi = "10.1515/IJNSNS.2007.8.3.385",

language = "English",

volume = "8",

pages = "385--392",

journal = "International Journal of Nonlinear Sciences and Numerical Simulation",

issn = "1565-1339",

publisher = "Walter de Gruyter GmbH",

number = "3",

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TY - JOUR

T1 - Direct solutions of N-th order initial value problems in decomposition series

AU - Yahaya, F.

AU - Hashim, I.

AU - Ismail, E. S.

AU - Zulkifle, A. K.

PY - 2007

Y1 - 2007

N2 - In this paper, a class of linear and non-linear nth-order initial value problems (IVPs) is considered. The solutions of these IVPs are obtained by adapting the modified Adomian decomposition method (MADM) as an algorithm for approximating the solutions of the equations in a sequence of time intervals (i.e. time steps). In this way the series solutions are valid for quite a long time span. Several test cases are chosen to demonstrate the performance of the multistage modified Adomian decomposition method (MMADM).

AB - In this paper, a class of linear and non-linear nth-order initial value problems (IVPs) is considered. The solutions of these IVPs are obtained by adapting the modified Adomian decomposition method (MADM) as an algorithm for approximating the solutions of the equations in a sequence of time intervals (i.e. time steps). In this way the series solutions are valid for quite a long time span. Several test cases are chosen to demonstrate the performance of the multistage modified Adomian decomposition method (MMADM).

KW - Adomian decomposition method

KW - Initial value problems

KW - Series solution

UR - https://www.scopus.com/pages/publications/34548575151

U2 - 10.1515/IJNSNS.2007.8.3.385

DO - 10.1515/IJNSNS.2007.8.3.385

M3 - Article

AN - SCOPUS:34548575151

SN - 1565-1339

VL - 8

SP - 385

EP - 392

JO - International Journal of Nonlinear Sciences and Numerical Simulation

JF - International Journal of Nonlinear Sciences and Numerical Simulation

IS - 3

ER -

Direct solutions of N-th order initial value problems in decomposition series

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Keywords

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