On a new reliable modification of homotopy analysis method

A. Sami Bataineh; M. S.M. Noorani; I. Hashim

doi:10.1016/j.cnsns.2007.10.007

On a new reliable modification of homotopy analysis method

A. Sami Bataineh
, M. S.M. Noorani
, I. Hashim

Universiti Kebangsaan Malaysia

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

92 Scopus citations

Abstract

In this paper, a new modification of the homotopy analysis method (HAM) is presented and applied to homogeneous or non-homogeneous differential equations with constant or variable coefficients. A comparative study between the new modified homotopy analysis method (MHAM) and the classical HAM is conducted. The main advantage of MHAM is that one can avoid the uncontrollability problems of the non-zero endpoint conditions encountered in the traditional HAM. Several illustrative examples are given to demonstrate the effectiveness and reliability of MHAM.

Original language	English
Pages (from-to)	409-423
Number of pages	15
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	14
Issue number	2
DOIs	https://doi.org/10.1016/j.cnsns.2007.10.007
State	Published - Feb 2009
Externally published	Yes

Keywords

Homotopy analysis method
Modified homotopy analysis method
Non-linear equations

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10.1016/j.cnsns.2007.10.007

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title = "On a new reliable modification of homotopy analysis method",

abstract = "In this paper, a new modification of the homotopy analysis method (HAM) is presented and applied to homogeneous or non-homogeneous differential equations with constant or variable coefficients. A comparative study between the new modified homotopy analysis method (MHAM) and the classical HAM is conducted. The main advantage of MHAM is that one can avoid the uncontrollability problems of the non-zero endpoint conditions encountered in the traditional HAM. Several illustrative examples are given to demonstrate the effectiveness and reliability of MHAM.",

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T1 - On a new reliable modification of homotopy analysis method

AU - Sami Bataineh, A.

AU - Noorani, M. S.M.

AU - Hashim, I.

PY - 2009/2

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N2 - In this paper, a new modification of the homotopy analysis method (HAM) is presented and applied to homogeneous or non-homogeneous differential equations with constant or variable coefficients. A comparative study between the new modified homotopy analysis method (MHAM) and the classical HAM is conducted. The main advantage of MHAM is that one can avoid the uncontrollability problems of the non-zero endpoint conditions encountered in the traditional HAM. Several illustrative examples are given to demonstrate the effectiveness and reliability of MHAM.

AB - In this paper, a new modification of the homotopy analysis method (HAM) is presented and applied to homogeneous or non-homogeneous differential equations with constant or variable coefficients. A comparative study between the new modified homotopy analysis method (MHAM) and the classical HAM is conducted. The main advantage of MHAM is that one can avoid the uncontrollability problems of the non-zero endpoint conditions encountered in the traditional HAM. Several illustrative examples are given to demonstrate the effectiveness and reliability of MHAM.

KW - Homotopy analysis method

KW - Modified homotopy analysis method

KW - Non-linear equations

UR - https://www.scopus.com/pages/publications/47749140021

U2 - 10.1016/j.cnsns.2007.10.007

DO - 10.1016/j.cnsns.2007.10.007

M3 - Article

AN - SCOPUS:47749140021

SN - 1007-5704

VL - 14

SP - 409

EP - 423

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 2

ER -

On a new reliable modification of homotopy analysis method

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Keywords

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