Modified homotopy analysis method for solving systems of second-order BVPs

“…HAM serves to be a signi cant technique to solve many interesting problems [23][24][25]. Several modi cations in the vibrant HAM has been proposed till present, such as, modi ed homotopy analysis method (MHAM) [26,27], Spectral homotopy analysis method (SHAM) [28,29], optimal homotopy analysis method (OHAM) [30,31], Predictor homotopy analysis method (PHAM) [32,33], fractional homotopy analysis transform method (FHATM) [34,35], etc.…”

Section: Introductionmentioning

confidence: 99%

Investigation of combined heat and mass transfer between vertical parallel plates in a two-layer flow of couple stress nanofluid

et al. 2016

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Abstract:This study is an investigation of fully-developed laminar ow in a two-layer vertical channel; one part lled with couple stress nano uid and the other part with clear couple stress uid. The ow is examined for combined heat and mass transfer using uniform wall temperature and concentration boundary conditions. Optimal homotopy analysis method (OHAM) is used to solve the nonlinear coupled ordinary di erential equations (ODEs) governing the ow in each region. This method is based on the homotopy analysis method (HAM) which is an e ective method to analytically approximate the solution of highly nonlinear problems. The in uence of pertinent parameters is observed on velocity, temperature, and concentration distributions, speci cally, the e ect of Brownian parameter on couple stress uid is mentioned.

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“…In [10] also, the author has provided the variational iteration method to further investigation to the aforementioned system. Furthermore, the homotopy analysis method has been applied to solve system (1) and (2) as described in [11]. Finally, the B-spline method for solving the linear form of system (1) is proposed recently in [12].…”

Section: Introductionmentioning

confidence: 99%

Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

Arqub¹,

Abo-Hammour²,

Momani³

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper, a numerical algorithm, based on the use of genetic algorithm technique, is presented for solving a class of nonlinear systems of second-order boundary value problems. In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraints boundary condtions, and is then solved using continuous genetic algorithm. In general, the proposed technique uses smooth operators and avoids sharp jumps in the parameter values. The applicability, efficiency, and accuracy of the proposed algorithm for the solution of different problems is investigated. Meanwhile, the convergence analysis based on the resulting statistical data is also discussed.

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Modified homotopy analysis method for solving systems of second-order BVPs

Cited by 79 publications

References 31 publications

Solution of Higher Order Partial Differential Equation by using Homotopy Analysis Method

Solution of Higher Order Partial Differential Equation by using Homotopy Analysis Method

Investigation of combined heat and mass transfer between vertical parallel plates in a two-layer flow of couple stress nanofluid

Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

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