Solution of Parabolic Partial Differential Equations Via Non-Polynomial Cubic Spline Technique

Ahmad, B. H.; Perviz, Anjum; Ahmad, Maqbool; Dayan, Fazal

doi:10.32350/sir/53.05

Cited by 4 publications

(5 citation statements)

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“…In Figure (8) the actions that were taken on the concentration profile are discussed for different parameters.…”

Section: Resultsmentioning

confidence: 99%

“…( 1) is satisfied identically by employing transformation, from eq(2, 3, 4) converted into nonlinear ordinary differential equations from eq. (7,8,9).…”

Section: Research Questionsmentioning

confidence: 99%

“…[5] investigated the impact of MHD effects shape of the nanoparticles and thermal radiations through the sheet. Many other researchers like [6,7,8] are also worked out for nanofluid flow.…”

Section: Introductionmentioning

confidence: 99%

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The Role of External Heat Sources and Chemical Reactions for Enhanced Heat Transfer through Maxwell Nanofluid Flow

ahmad,

Ali,

Bariq

et al. 2023

Preprint

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This research addresses finding the dynamics of heat transfer in two-dimensional MHD Maxwell nanoflu-ids flow under the influence of mixed convection and activation energy. The heat source is strategically positioned to take advantage of convective heat transfer and increase the overall thermal performance. Numerical simulations employing computational fluid dynamics (CFD) approaches are used to evaluate the improved thermal transfer efficiency. The governing equations, which comprise the continuity, momentum, energy, and species transport equations, are addressed using appropriate similarity transformations acquired from a PDE (Partial differential equations) model that has been turned into an ODE(ordinary differential equations). MATLAB is used to solve such a nonlinear ODE model. The effects of many parameters, such as nanoparticle concentration, the intensity of an external heat source, and chemical reaction speeds, are intentionally explored. The fluid flow declaration is evaluated in terms of viscosity, and porosity. It was discovered that increasing inputs of rotation, porosity factor, activation energy, and magnetic effect resulted in a significant increase in the profile of temperature. The variational patterns of Nusselt number and skin friction are numerically performed at a rectangular stretching surface.

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“…In Figure (8) the actions that were taken on the concentration profile are discussed for different parameters.…”

Section: Resultsmentioning

confidence: 99%

“…( 1) is satisfied identically by employing transformation, from eq(2, 3, 4) converted into nonlinear ordinary differential equations from eq. (7,8,9).…”

Section: Research Questionsmentioning

confidence: 99%

See 1 more Smart Citation

The Role of External Heat Sources and Chemical Reactions for Enhanced Heat Transfer through Maxwell Nanofluid Flow

ahmad,

Ali,

Bariq

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…These methods include variational iteration method [34], variational iteration algorithm-I with an auxiliary parameter [3], the differential transform method [11], A fourth-order finite difference scheme [12], the discrete Adomian decomposition method [7], the residual power series [42], the finite difference method [23], non-polynomial cubic spline method [4], extended cubic B-spline approximation [6], finite-difference MacCormack method [17], C 1 Cubic quasi-interpolation splines [10], differential transform method and Padé approximant [43], double Laplace transform and double Laplace decomposition methods [31]. Many mathematicians have solved such problems to date, for more details, see [1,5,8,9,13,24,25,27,35]. Few authors have studied the spline method to solve partial differential equations, for instance, in [2,21,22,30,32,36,37,40].…”

Section: Introductionmentioning

confidence: 99%

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Mahmood¹,

Tahir²,

Jwamer³

2023

J. Math. Computer Sci.

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In this work, some types of nonlinear parabolic partial differential equations have been studied by means of the collocation method with cubic B-splines, without transformation or linearization. Here, the convergence analysis of the current scheme is also theoretically investigated. A few numerical examples are given to illustrate the viability and effectiveness of the proposed technique. The error norms l 2 and l ∞ are used to assess the accuracy of the current method. In this respect, the proposed method, keeping the real features of such problems, is able to save the behavior of nonlinear terms without facing any conventional drawbacks. Furthermore, it is mathematically shown and numerically seen that there is a good agreement between the approximation and the exact solutions. The current approach reduces the cost of calculation as well as the need for storage space at various parameters.

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“…Based on different approaches (such as classical spline, spline with knots, and fractal spline) various monotonicity-preserving models for monotone data have been discussed in the previous literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Spline functions have also been used for the solution of partial differential equations [19,20]. Previously, spline functions have become the main tools for solving monotonicity problems.…”

Section: Introductionmentioning

confidence: 99%

Monotone Data Modelling Using Rational Cubic Fractal Interpolation Function

2023

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Geometric modelling of several intricate and complex structures such as trees, mountains, clouds, ferns, geographic topography, and coastlines is challenging in computer graphics. Traditional splines such astrigonometric, polynomial, exponential, and rational fail to simulate this significant class of complex structures, which are highly irregular in nature. For this purpose, this research develops a novel cutting-edgemethod for synthesizing and modelling structures. The proposed technique; C 1 fractal interpolation function (FIF) builds an iterated function system (IFS) by integrating fractal calculus and rational cubic polynomial functions. Appropriate conditions on scaling and shape parameters are derived to help maintain the inherited shape qualities of the data. Experiments in numerous scientific domains, such as the pharmaceutical and chemical industries have been presented as an example, to confirm the usefulness of the suggested model. Moreover, the graphic results demonstrated that the developed monotone hybrid model (MHM) offers a heterogeneous method for gathering data with a monotone structure.

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Solution of Parabolic Partial Differential Equations Via Non-Polynomial Cubic Spline Technique

Cited by 4 publications

References 0 publications

The Role of External Heat Sources and Chemical Reactions for Enhanced Heat Transfer through Maxwell Nanofluid Flow

The Role of External Heat Sources and Chemical Reactions for Enhanced Heat Transfer through Maxwell Nanofluid Flow

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Monotone Data Modelling Using Rational Cubic Fractal Interpolation Function

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