Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers

Natesan, Srinivasan; Jayakumar, J. S.; Vigo‐Aguiar, Jesús

doi:10.1016/s0377-0427(03)00476-x

Cited by 61 publications

(25 citation statements)

References 9 publications

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“…To estimate the error and compute the rate of convergence in the computed numerical solution, the double mesh principle was used [18,21,24]. As the exact solution of the problem was unknown, and therefore to approximate the pointwise errors |(˜ − )(η i )|; i = 0, 1, 2, .…”

Section: Double Mesh Principlementioning

confidence: 99%

Simulation of Natural Convective Boundary Layer Flow of a Nanofluid Past a Convectively Heated Inclined Plate in the Presence of Magnetic Field

Goyal

Bhargava

2018

Int. J. Appl. Comput. Math

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This paper deals with the numerical simulation of transient magnetohydrodynamics natural convective boundary layer flow of a nanofluid over an inclined plate. In the modeling of nanofluids, dynamic effects including the Brownian motion and thermophoresis are taken into account. Numerical solutions have been computed via the Galerkin-finite element method. The effects of angle of inclination, buoyancy-ratio parameter, Brownian motion, thermophoresis and magnetic field are taken into account and controlled by nondimensional parameters. To compute the rate of convergence and error of the computed numerical solution, the double mesh principle is used. Similarity solutions are calculated and presented graphically for non-dimensional velocity, temperature, local rate of heat and mass transfer with pertinent parameters. The modified Nusselt number decreases with increasing inclination angle, buoyancy-ratio parameter, Brownian motion and thermophoresis parameter, whereas it increases with increasing Prandtl number. Validation of the results is achieved with earlier results for forced convective flow and non-magnetic studies. Such problems have several applications in engineering and petroleum industries such as electroplating, chemical processing of heavy metals and solar water heaters. External magnetic fields play an important role in electrical power generation, inclination/acceleration sensors, fine-tuning of the final materials to industrial specification because of their controlling behaviour on the flow characteristics of nanofluids.

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Section: Double Mesh Principlementioning

confidence: 99%

Simulation of Natural Convective Boundary Layer Flow of a Nanofluid Past a Convectively Heated Inclined Plate in the Presence of Magnetic Field

Goyal

Bhargava

2018

Int. J. Appl. Comput. Math

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“…Motivated by the works of Leung [2], Jian-ping and Zong-chi [4], Mo and Wen [9] and Natesan et al [15], we consider the following boundary value problem for singularly perturbed third order differential equation with a turning point at x = 0:…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…In [11] Kadalbajoo and Patidar applied a numerical method based on cubic spline with nonuniform grid for a second order SPTPP. Natesan et al [15] proposed a parameter uniform numerical method in which piecewise-uniform mesh is combined with classical finite difference scheme to obtain the numerical solution. For more detail one may refer [18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Parameter Uniform Numerical Method for Third Order Singularly Perturbed Turning Point Problems Exhibiting Boundary Layers

Geetha

Tamilselvan

Subburayan

2015

Int. J. Appl. Comput. Math

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“…Such behavior results in some major computational difficulties in the numerical treatment of singularly perturbed problems. Standard finite difference or finite element methods used on uniform meshes can not obtain accurate approximate solutions and in recent years a large number of special-purpose methods have been proposed [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, there are only a few results concerning numerical solutions of singularly perturbed turning point problems. Natesan et al [1] proposed a parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers. Kadalbajoo et al [2] solved stiff singularly perturbed turning point problem having twin boundary layers by a collocation method.…”

Section: Introductionmentioning

confidence: 99%

A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method

Geng

Qian

2016

Calcolo

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In this paper, a simple numerical method is proposed for solving singularly perturbed boundary layers problems exhibiting twin boundary layers. The method avoids the choice of fitted meshes. Firstly the original problem is transformed into a new boundary value problem whose solution does not change rapidly by a proper variable transformation; then the transformed problem is solved by using the reproducing kernel method. Two numerical examples are given to show the effectiveness of the present method.

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Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers

Cited by 61 publications

References 9 publications

Simulation of Natural Convective Boundary Layer Flow of a Nanofluid Past a Convectively Heated Inclined Plate in the Presence of Magnetic Field

Simulation of Natural Convective Boundary Layer Flow of a Nanofluid Past a Convectively Heated Inclined Plate in the Presence of Magnetic Field

Parameter Uniform Numerical Method for Third Order Singularly Perturbed Turning Point Problems Exhibiting Boundary Layers

A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method

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