Exact solution of coupled 1D non-linear Burgers’ equation by using Homotopy Perturbation Method (HPM): A review

Kapoor, Mamta

doi:10.1088/2399-6528/abb218

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…On the contrary, the system of the peripheral region cannot be solved exactly, so we adopted the scheme of perturbation (HPM) [46][47][48] in which the same linear operator is chosen for velocity, heat, and energy functions, i.e., H � z 2 /zr 2 + 1/rz/zr. After using the routine calculation of HPM, the final solutions have been composed in subsequent forms:…”

Section: Solution Methodsmentioning

confidence: 99%

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

Zeeshan

Riaz

Alzahrani

et al. 2022

Mathematical Problems in Engineering

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Biologically inspired micropumps using the phenomena of peristalsis are highly involved in targeted drugging in pharmacological engineering. This study analyzed theoretically the transport of two immiscible fluids in a long flexible tube. The core region contains Johnson–Segalman non-Newtonian fluid, while the peripheral region is saturated by nanofluid. It is assumed that Darcy’s porous medium is encountered close to the walls of the tube. A complex peristaltic wave is transmitted on the compliant wall which induces the flow. Equations of continuity, momentum, energy, and nanoparticle concentration are used in modelling the problem. The modelled problem for both the regions, i.e., core and peripheral regions are developed with the assumptions of long wavelength and creeping flow. Temperature, velocity, and shear stress at the interface are assumed to be equal. The system of equations is solved analytically. The graphical results for different involving parameters are displayed and thoroughly discussed. It is received that the heat transfer goes inverse with fluid viscosity in the peripheral region, but opposite measurements are obtained in the core region. This theoretical model may be considerable in some medical mechanisms such as targeted drug delivery, differential diagnosis, and hyperthermia. Moreover, no study on non-Newtonian nanofluid is reported yet for the two-layered flow system, so this study will give a good addition in the literature of biomedical research.

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Section: Solution Methodsmentioning

confidence: 99%

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

Zeeshan

Riaz

Alzahrani

et al. 2022

Mathematical Problems in Engineering

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“…Several integral transforms are developed, such as: the Sumudu transform, Elzaki transform, Natural transform, Pourreza transform, G-transform, Sawi transform, Shehu transform, and others [1][2][3][4][5][6][7][8][9]. These transforms provided in the literature are applied to solve several integral equations, ODEs, PDEs, and fractional PDEs [10][11][12][13][14][15][16][17]. Fusion of these transforms with semi-analytical techniques such as ADM, DTM, HPM, and VIM can also create novel and efficient regimes to solve such equations [18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions

2022

Self Cite

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In the present research paper, an iterative approach named the iterative Shehu transform method is implemented to solve time-fractional hyperbolic telegraph equations in one, two, and three dimensions, respectively. These equations are the prominent ones in the field of physics and in some other significant problems. The efficacy and authenticity of the proposed method are tested using a comparison of approximated and exact results in graphical form. Both 2D and 3D plots are provided to affirm the compatibility of approximated-exact results. The iterative Shehu transform method is a reliable and efficient tool to provide approximated and exact results to a vast class of ODEs, PDEs, and fractional PDEs in a simplified way, without any discretization or linearization, and is free of errors. A convergence analysis is also provided in this research.

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“…Finally, they concluded that numeri-cal experiments demonstrate that the present method has potential for real engineering problems. Kapoor 24 has offered a review of the Homotopy perturbation method to fetch the analytical solution of coupled 1D non-linear Burgers equation. The author has attained the exact solution of the coupled 1D Burgers equation in the system of a power series (convergent in nature).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the coupled Burgers equation by trigonometric B‐spline collocation method

Uçar

Yağmurlu

YİĞİT

2022

Math Methods in App Sciences

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In the present study, the coupled Burgers equation is going to be solved numerically by presenting a new technique based on collocation finite element method in which cubic trigonometric and quintic B-splines are used as approximate functions. In order to support the present study, three test problems given with appropriate initial and boundary conditions are going to be investigated. The newly obtained results are compared with some of the other published numerical solutions available in the literature. The accuracy of the proposed method is discussed by computing the error norms L 2 and L ∞ . A linear stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.

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Exact solution of coupled 1D non-linear Burgers’ equation by using Homotopy Perturbation Method (HPM): A review

Cited by 5 publications

References 24 publications

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions

Numerical solution of the coupled Burgers equation by trigonometric B‐spline collocation method

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