Study of predictor corrector block method via multiple shooting to Blasius and Sakiadis flow

Majid, Zanariah Abdul; See, Phang Pei

doi:10.1016/j.amc.2017.06.038

Cited by 7 publications

(10 citation statements)

References 3 publications

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“…without reducing it to a system of first order equation. In Tables II, III and IV we compare our results of f (η), f (η) and f (η) respectively, with [17] and reference therein. Table V, we compare our results with [11].…”

Section: Numerical Resultsmentioning

confidence: 89%

“…In Table I, we compare our results for f (η) with results of [12] and give relative errors. The authors of [17] solved Blasius equation by using predictor corrector two-point block method. The main motivation of their study was to provide a new method that can solve the higher order boundary value problem directly without reducing it to a system of first order equation.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Xu and Guo applied the fixed point method to obtain the semi-analytical solution to Blasius equation [16]. A predictor corrector two-point block method is proposed to solve the well-know Blasius and Sakiadis flow numerically [17]. All these methods have their own shortcomings.…”

Section: Introductionmentioning

confidence: 99%

“…The authors of [17] solved Blasius equation by using predictor corrector two-point block method. The main motivation of their study was to provide a new method that can solve the higher order boundary value problem directly…”

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confidence: 99%

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A Neural Network Study of Blasius Equation

Mutuk

2020

Neural Process Lett

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In this work we applied a feed forward neural network to solve Blasius equation which is a thirdorder nonlinear differential equation. Blasius equation is a kind of boundary layer flow. We solved Blasius equation without reducing it into a system of first order equation. Numerical results are presented and a comparison according to some studies is made in the form of their results. Obtained results are found to be in good agreement with the given studies. I. * Electronic address: halilmutuk@gmail.com arXiv:1811.08936v1 [cs.LG] 8 Nov 2018 * The neural network based solution of a differential equation is differentiable and is in closed analytic form that can be used in any subsequent calculation. On the other hand most other techniques offer a discrete solution or a solution of limited differentiability. * Trial solutions of ANN include a single independent variable regardless of the dimension of the problem. * The neural network based method to solve a differential equation provides a solution with very good generalization properties. * The solutions are continuous over all the domain of the integration. Traditional numerical methods provide solutions over discrete points and the solution among these points must be interpolated. * The required number of model parameters is far less than any other solution technique and therefore, compact solution models are obtained, with very low demand on memory space. * The method is general and can be applied to ordinary differential equations (ODEs), systems of ODEs and to partial differential equations (PDEs) as well. * The method is general and can be applied to the systems defined on either orthogonal box boundaries or on irregular arbitrary shaped boundaries. * The method can be realized in hardware, using neuroprocessors, and hence offer the opportunity to tackle in real time difficult differential equation problems arising in many engineering applications. * The method can also be implemented on parallel architectures.

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Section: Numerical Resultsmentioning

confidence: 89%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A Neural Network Study of Blasius Equation

Mutuk

2020

Neural Process Lett

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“…However, the application of block methods to specific fluid model equations is not widely known. The study by Majid and See 28 used a predictor‐corrector two‐point block method to solve the Blasius and Sakiadis flow problem modeled as a third‐order boundary value problem, while Reference 29 investigated the heat transfer in a convective fin modeled as a second‐order boundary value problem using a hybrid block method. Recently, Reference 30 developed an implicit two‐step Obrechkoff‐type block method to solve the problem of unsteady sedimentation of spherical particles in Newtonian fluid media.…”

Section: Introductionmentioning

confidence: 99%

On a new block method for an MHD nanofluid flow with an exponentially decaying internal heat generation

Oyelakin

Adeyeye

Sibanda

et al. 2021

Numerical Methods in Fluids

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This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow and heat transfer characteristics between an actively controlled (AC) and a passively controlled (PC) nanoparticle concentration boundary is considered. The boundary value partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The system of ODEs is solved using a new block method without having to reduce the equivalent system to first‐order equations. The solutions are verified using the spectral local linearization method and further validation of the results is confirmed by comparing the current results, for some limiting cases, with those in existing literature. The solutions obtained using the block method are in good agreement with the solution obtained using the spectral local linearization method. The results are in good agreement with existing findings in previous studies. The solutions obtained using the AC and PC nanoparticle concentration boundary conditions are analyzed.

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An analytical self‐consistent method for different forms of the Blasius equation

Yasuri

2022

Math Methods in App Sciences

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Nonlinear Blasius equation of boundary layer plays a crucial role in different physics and engineering fields. For nearly a century, researchers have been trying to find a convergent and closed analytical solution of the Blasius equation. In this paper, an analytical self‐consistent method (ASCM) is presented to solve this equation. Then, the method was implemented in other forms of Blasius equation, that is, Sakiadis flow and shrinking sheet problem. The analytical solutions obtained show the success of ASCM and agree closely with the corresponding numerical results. The reliability and efficiency of the proposed method are demonstrated on the numerical experiments.

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Study of predictor corrector block method via multiple shooting to Blasius and Sakiadis flow

Cited by 7 publications

References 3 publications

A Neural Network Study of Blasius Equation

A Neural Network Study of Blasius Equation

On a new block method for an MHD nanofluid flow with an exponentially decaying internal heat generation

An analytical self‐consistent method for different forms of the Blasius equation

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