Approximate Solution of Nonlinear System of BVP Arising in Fluid Flow Problem

Alomari, A. K.; Anakira, N. R.; Bataineh, A. Sami; Hashim, Ishak

doi:10.1155/2013/136043

Cited by 25 publications

(28 citation statements)

References 14 publications

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“…This procedure give us with a convenient way to control the convergence of approximation series and demonstrates its validity and potential efficiency to solve a wide class of problems in applied science and engineering and also valid for small parameters. In the last few years, OHAM and its modifications has been applied successfully to solve many types of differential equations [12,13,14,15,16,17,18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

An Accurate Approximate Solutions of Multipoint Boundary Value Problems

Anakira¹,

Al-Shorman²,

Jameel³

2019

(GLM)

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The main objective of this paper is to obtain a new accurate approximate solutions for a kind of ordinary differential equations called multipoint boundary value problems by using simple modification of optimal homotopy asymptotic method (OHAM). This procedure is a well-performance for calculating a better approximate solutions using one-order of approximation comparing with other methods which need higher order of approximations to gives the same results. Some examples are presented to testify the accuracy and applicability of this procedure. Comparisons are made between the present procedure and the other methods.

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Section: Introductionmentioning

confidence: 99%

An Accurate Approximate Solutions of Multipoint Boundary Value Problems

Anakira¹,

Al-Shorman²,

Jameel³

2019

(GLM)

View full text Add to dashboard Cite

show abstract

“…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%

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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“…These problems can be formulated either as a system of ordinary or partial differential equations [6,15,24]. Fuzzy differential equations (FDEs) are a useful tool to model a dynamical system when information about its behavior is inadequate.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of nth order fuzzy initial value problems by six stages

Jameel¹,

Anakira²,

Alomari³

et al. 2016

J. Nonlinear Sci. Appl.

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The purpose of this paper is to present a numerical approach to solve fuzzy initial value problems (FIVPs) involving n-th order ordinary differential equations. The idea is based on the formulation of the six stages Runge-Kutta method of order five (RKM56) from crisp environment to fuzzy environment followed by the stability definitions and the convergence proof. It is shown that the n-th order FIVP can be solved by RKM56 by transforming the original problem into a system of first-order FIVPs. The results indicate that the method is very effective and simple to apply. An efficient procedure is proposed of RKM56 on the basis of the principles and definitions of fuzzy sets theory and the capability of the method is illustrated by solving second-order linear FIVP involving a circuit model problem.

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Approximate Solution of Nonlinear System of BVP Arising in Fluid Flow Problem

Cited by 25 publications

References 14 publications

An Accurate Approximate Solutions of Multipoint Boundary Value Problems

An Accurate Approximate Solutions of Multipoint Boundary Value Problems

Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems

Numerical solution of nth order fuzzy initial value problems by six stages

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