The solution of multipoint boundary value problems by the Optimal Homotopy Asymptotic Method

Javed, Ali; Islam, Saeed; Islam, Sharmin; Zaman, Gul

doi:10.1016/j.camwa.2009.12.002

Cited by 58 publications

(42 citation statements)

References 22 publications

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“…In this section, we review the fundamental principles of OHAM as explained in Marinca et al [20] and other researcher [1,16]. Consider the IVP…”

Section: Optimal Homotopy Asymptotic Methods (Oham)mentioning

confidence: 99%

“…The validity and the applicability of OHAM is independent whether there exist small parameters in the governing equation or not. In a series of papers, several authors [1,4,5,8,10,12,14,15,16,18,19,24,25] have proved effectiveness, reliability and generalization of this method and obtained solutions of currently important applications in science and engineering.…”

Section: Introductionmentioning

confidence: 99%

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Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems

Anakira¹,

Alomari²,

Jameel³

et al. 2016

J. Nonlinear Sci. Appl.

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In this paper, a new approximate analytical algorithm namely multistage optimal homotopy asymptotic method (MOHAM) is presented for the first time to obtain approximate analytical solutions for linear, nonlinear and system of initial value problems (IVPs). This algorithm depends on the standard optimal homotopy asymptotic method (OHAM), in which it is treated as an algorithm in a sequence of subinterval. The main advantage of this study is to obtain continuous approximate analytical solutions for a long time span. Numerical examples are tested to highlight the important features of the new algorithm. Comparison of the MOHAM results, standard OHAM, available exact solution and the fourth-order Runge Kutta (RK4) reveale that this algorithm is effective, simple and more impressive than the standard OHAM for solving IVPs.Keywords: Optimal homotopy asymptotic method (OHAM), multistage optimal homotopy asymptotic method (MOHAM), initial value problems, series solution, Mathematica 9. 2010 MSC: 65M10, 78A48.

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“…In this section, we review the fundamental principles of OHAM as explained in Marinca et al [20] and other researcher [1,16]. Consider the IVP…”

Section: Optimal Homotopy Asymptotic Methods (Oham)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems

Anakira¹,

Alomari²,

Jameel³

et al. 2016

J. Nonlinear Sci. Appl.

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show abstract

“…Example 2 Consider the following nonlinear three-point BVP [1,20,49,54,58]: A comparison of the approximate solutions obtained by the present method for N = 10 and the other methods is described in Table 3, from which we can see that the results of our computations are in good agreement with the results obtained by the ADM [54], SCM [49], OHAM [1], RKM [20] and successive iteration method (SIM) [58]. In particular, the numerical results of our method is totally the same as those of the OHAM with the digits used in Table 3.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Dehghan and his research group proposed the Adomian decomposition method (ADM) [54], variational iteration method (VIM) [55], homotopy analysis method (HAM) [9], Sinc-collocation method (SCM) [49] to solve the muti-point BVPs. In [1], the solution of multi-point BVPs was considered by using the optimal homotopy asymptotic method (OHAM). Geng and Cui [21] solved a class of the second-order muti-point BVPs by combining the VIM and the homotopy perturbed method (HPM).…”

Section: Introductionmentioning

confidence: 99%

A new algorithm based on differential transform method for solving multi-point boundary value problems

Xie

Zhou

2015

International Journal of Computer Mathematics

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In this work, an efficient algorithm based on the differential transform method is applied to solve the multi-point boundary value problems. The solution obtained by using the proposed method takes the form of a convergent series with easily computable components. Several numerical examples, both linear and nonlinear, are given to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods.

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“…Researchers developed many methods to address this issue and to obtain approximate solutions of high accuracy. The most common techniques for obtaining a series form of the approximate solution, are; Adomian Decomposition Method (ADM) [3][4][5], variational iteration [6][7][8], homotopy perturbation [9][10][11], homotopy analysis [12], Differential Transform Method (DTM) [13] and optimal homotopy asymptotic method [14,15].…”

Section: Introductionmentioning

confidence: 99%

Application of New Iterative Method and Adomian Decomposition Method to Hamel’s Flow Problem

Javed¹

2017

JACE

Self Cite

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In this work, we solve the Hamel's Problem using New Iterative Method (NIM) and Adomian Decomposition Method (ADM). This is a third order nonlinear boundary value problem. This problem arises when an incompressible fluid flows outward in a trough between two nonparallel plane walls. Application of these methods to this problem gives excellent numerical results with only three iterations. Moreover, accompanying residuals with these methods is an additional plus point which make these methods self-sufficient.

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The solution of multipoint boundary value problems by the Optimal Homotopy Asymptotic Method

Cited by 58 publications

References 22 publications

Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems

Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems

A new algorithm based on differential transform method for solving multi-point boundary value problems

Application of New Iterative Method and Adomian Decomposition Method to Hamel’s Flow Problem

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