Polynomial differential quadrature method for numerical solutions of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients

Jiwari, Ram; Gupta, Rishabh; Kumar, Vikas

doi:10.1016/j.asej.2014.06.005

Cited by 34 publications

(31 citation statements)

References 38 publications

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“…In this segment, we exhibit the computational technique employed to solve the nonlinear system of PDEs (14)- (15) with boundary conditions (16). Newton's linearization method (NLM) was utilized to linearize the non-linear system (14)- (16), which was subsequently solved using the differential quadrature method (DQM) [27][28][29][30][31][32][33][34][35][36][37][38][39] and two-point backward finite difference method. Applying NLM on (14)- (16) gives:…”

Section: Hybrid Linearization-differential Quadrature Methods (Hldqm)mentioning

confidence: 99%

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

2019

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The spotlight of this investigation is primarily the effectiveness of the magnetic field on the natural convective for a Fe 3 O 4 ferrofluid flow over a vertical radiate plate using streamwise sinusoidal variation in surface temperature. The energy equation is reduplicated by interpolating the non-linear radiation effectiveness. The original equations describing the ferrofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-differential quadrature method (HLDQM). HLDQM is a high order semi-analytical numerical method that results in analytical solutions in η-direction, and so the solutions are valid overall in the η domain, not only at grid points. The dimensionless velocity and temperature curves are elaborated. Furthermore, the engineering curiosity of the drag coefficient and local Nusselt number are debated and sketched in view of various emerging parameters. The analyzed numerical results display that applying the magnetic field to the ferroliquid generates a dragging force that diminishes the ferrofluid velocity, whereas it is found to boost the temperature curves. Furthermore, the drag coefficient sufficiently minifies, while an evolution in the heat transfer rate occurs as nanoparticle volume fraction builds. Additionally, the augmentation in temperature ratio parameter signifies a considerable growth in the drag coefficient and Nusselt number. The current theoretical investigation may be beneficial in manufacturing processes, development of transport of energy, and heat resources. Mathematics 2019, 7, 1014 2 of 12 naturalistic kind of boundary condition which considers the effectiveness of thermophoresis Brownian movement. Khan and Pop [4] utilized the idea in [3] to contemplate the principal deal with nanofluid flow over an extending sheet. Bachok et al. [5] implemented an investigation of nanofluid flow past a semi-infinite plate. Rashad et al. [6] inspected the enhancement of heat transfer in a Darcy nanofluid convective flow past a porous cone. Rashad et al. [7] also probed the non-Darcy problem of a thermally stratified nanofluid flow over a vertical cylinder. They explored how heat transfer rate declined as the Brownian motion parameter boosted. However, abundant fundamental investigations are performed in this field, as can be seen in [8-13].Magnetic nanofluids (or ferrofluids) are the colloidal suspension of magneto-nanoparticles in a regular fluid (water, kerosene, mineral oil). Ferrofluids are magnetically controllable nanofluids, which contain magnetic nanoparticles, such as iron, cobalt, nickel, magnetite, ferrite, spinel-type. Since ferrofluids can be easily manipulated by means of an external magnetic force, the use of these fluids is promoted in numerous significant industrial applications, such as in vacuum seals, vibration-dampers, loudspeakers, shock absorbers, transformers coolant, and stepper motors [14][15][16][17][18][19]. Hayat et al. [20,21] probed the magneto-flow of Newtonian and viscoelastic nanofluids over ...

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Section: Hybrid Linearization-differential Quadrature Methods (Hldqm)mentioning

confidence: 99%

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

2019

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“…The Fitzhugh-Nagumo (FN) equation has numerous applications in different fields such as branching brownian motion process, flame propagation, neurophysiology, logistic population growth and nuclear reactor theory [24]. Numerical solution of FN equation can be found in [23,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Local Formulation for Time–Dependent PDEs

et al. 2019

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In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation on regular and irregular domains.

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“…If = −1 in Eq(1), then the Newell-Whitehead-Segel(NWS) [23][24][25][26] is formed to be = − 1 − (2) and if = 0 the Zeldovich equation is formed. The Zeldovich equation [27] is represented as = + − (3) This study is motivated by the need to propose the (G'/G)-expansion method to construct exact analytical solutions of fractional reaction-diffusion equations in the sense of modified Riemann-Liouville derivative by Jumarie [28]. The Jumarie's modified Riemann-Liouville derivative of order is defined by the following expression: which will be used in the following sections.…”

Section: Introductionmentioning

confidence: 99%

“…Some useful formulas and results of Jumarie's modified Riemann-Liouville derivative were summarized in[27], four of them are )…”

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2018

IJMCT

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In this paper, the (G'/G)-expansion method for solving nonlinear fractional reaction-diffusion equations is introduced. (G'/G)-expansion method algorithm is tested on fractional Fitzhugh-Nagumo, Newell-Whitehead-Segel and Zeldovich equations. New types of exact analytical solutions are obtained with the help of symbolic computation. It is shown that the method provides a straightforward and mathematical tool for solving nonlinear fractional reaction-diffusion equations.

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Polynomial differential quadrature method for numerical solutions of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients

Cited by 34 publications

References 38 publications

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

An Efficient Local Formulation for Time–Dependent PDEs

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