A Novel Numerical Approach for Simulating the Nonlinear MHD Jeffery–Hamel Flow Problem

Adel, Waleed; Biçer, Kübra Erdem; Sezer, Mehmet

doi:10.1007/s40819-021-01016-3

Cited by 17 publications

(1 citation statement)

References 36 publications

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“…The operational matrix of Bernoulli polynomials has been studied in [31] by Zeghdane and then used to solve the stochastic integral equations. Also, Adel et al [32,33] employed the collocation method for solving the Emden Fowler and MHD Je ery-Hamel ow problems. All of these attempts prove that this method is e ective with high accuracy.…”

Section: Introductionmentioning

confidence: 99%

On numerical solutions of Telegraph, viscous, and modified Burgers equations via Bernoulli collocation method

Adel,

Rezazadeh,

Inc

2023

Scientia Iranica

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The presented work aims to develop a novel technique for obtaining the solution of linear and nonlinear Partial Di erential Equations (PDEs). This technique is based on applying a collocation method with the aid of Bernoulli polynomials and the use of such an algorithm to solve di erent types of PDEs. The method applies the regular nite di erence scheme to the main problem and transforms it into an algebraic system. The obtained system is then solved, the unknown coe cient is acquired, and an approximate solution for the problems is achieved. Some test results of famous equations, including the telegraph, viscous Burger, and modi ed Burger equations, are tested to ensure that the provided algorithm is e ective and robust. In addition, a comparison is provided with other recent techniques from the literature. The current technique proves to have high accuracy concerning the error measure and through graphical representation of the solution.

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Section: Introductionmentioning

confidence: 99%

On numerical solutions of Telegraph, viscous, and modified Burgers equations via Bernoulli collocation method

Adel,

Rezazadeh,

Inc

2023

Scientia Iranica

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A matrix technique‐based numerical treatment of a nonlocal singular boundary value problems

Sriwastav,

Barnwal,

Srivastav

et al. 2023

Math Methods in App Sciences

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The mathematical modeling of the decisive event of astrophysics, physiology, and many other areas of science and technology witness the involvement of singular boundary value problems. The nonlocal boundary conditions are more informative than local boundary conditions (initial conditions and two‐point boundary conditions) to evaluate some mathematical models. This article presents a collocation approach‐based matrix technique to approximate the solution of the fusion of a class of singular differential equations subject to nonlocal three‐point boundary conditions. The proposed strategy utilizes the truncation of the series expansion of a function belonging to in terms of Bernoulli polynomials. It transforms the singular boundary value problems into a set of nonlinear algebraic equations, which can be dealt with by any mathematical software. The Lipschitz condition on an equivalent completely continuous nonlinear operator has been used to prove the convergence analysis of the scheme. Some extremely nonlinear test examples are solved and provided in contrast with the exact solution. These numerical results are also examined against some existing numerical techniques to verify the applicability and significance of the proposed methodology. There are a few numerical examples that are application based but do not have exact solutions. In such cases, residual error norm is employed to measure the accuracy of the numerical strategies. The computational data demonstrate the superiority and validity of the proposed technique over existing numerical approaches.

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Nano-fluid flow predictions in convergent/divergent channels using ANN-BLMT and physics-informed neural networks

Aslam,

Shaukat,

Riaz

et al. 2024

J Therm Anal Calorim

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A Novel Numerical Approach for Simulating the Nonlinear MHD Jeffery–Hamel Flow Problem

Cited by 17 publications

References 36 publications

On numerical solutions of Telegraph, viscous, and modified Burgers equations via Bernoulli collocation method

On numerical solutions of Telegraph, viscous, and modified Burgers equations via Bernoulli collocation method

A matrix technique‐based numerical treatment of a nonlocal singular boundary value problems

Nano-fluid flow predictions in convergent/divergent channels using ANN-BLMT and physics-informed neural networks

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