The Experts below are selected from a list of 72 Experts worldwide ranked by ideXlab platform
Kuppalapalle Vajravelu - One of the best experts on this subject based on the ideXlab platform.
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A Method of Directly Defining the inverse Mapping for a HIV infection of CD4+ T-cells model
Applied Mathematics and Nonlinear Sciences, 2020Co-Authors: Mangalagama Dewasurendra, Ying Zhang, Noah Boyette, Ifte Islam, Kuppalapalle VajraveluAbstract:AbstractIn 2015, Shijun Liao introduced a new method of directly defining the inverse mapping (MDDiM) to approximate analytically a nonlinear differential equation. This method, based on the Homotopy Analysis Method (HAM) was proposed to reduce the time it takes in solving a nonlinear equation. Very recently, Dewasurendra, Baxter and Vajravelu (Applied Mathematics and Computation 339 (2018) 758–767) extended the method to a system of two nonlinear differential equations. In this paper, we extend it further to obtain the solution to a system of three nonlinear differential equations describing the HIV infection of CD4+ T-cells. In addition, we analyzed the advantages of MDDiM over HAM, in obtaining the numerical results. From these results, we noticed that the infected CD4+ T-cell density increases with the number of virions N; but decreases with the blanket death rate μI.
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Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer
2013Co-Authors: Kuppalapalle Vajravelu, Robert A. Van GorderAbstract:Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems and often fail when used for problems with strong nonlinearity. Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering.Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA.
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Corrigendum to "Existence and uniqueness results for a nonlinear differential equation arising in MHD Falkner-Skan flow" [Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 2272-2277]
Communications in Nonlinear Science and Numerical Simulation, 2012Co-Authors: Robert A. Van Gorder, Kuppalapalle VajraveluAbstract:Abstract We correct the hypothesis for which the existence and uniqueness theorems of Van Gorder and Vajravelu [Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 2272–2277] hold. This correction modifies the range of parameters valid under the given theorems.
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Existence and uniqueness results for a nonlinear differential equation arising in viscous flow over a nonlinearly stretching sheet
Applied Mathematics Letters, 2011Co-Authors: Robert A. Van Gorder, Kuppalapalle Vajravelu, F. Talay AkyildizAbstract:Abstract We establish the existence and uniqueness results for a class of nonlinear third order ordinary differential equations arising in the viscous flow over a nonlinearly stretching sheet. In particular, we consider solutions over the semi-infinite interval [ 0 , ∞ ) . These results generalize the results of Vajravelu and Cannon [K. Vajravelu, J.R. Cannon, Applied Mathematics and Computation 181 (2006) 609], where they considered the finite interval [ 0 , R ] . Also in this paper, we answer their open question of finding the existence and uniqueness results for the problem over the semi-infinite domain and discuss the properties of the solution.
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Comment on “Series solution of hydromagnetic flow and heat transfer with hall effect in a second grade fluid over a stretching sheet”
Open Physics, 2010Co-Authors: Robert A. Van Gorder, Kuppalapalle VajraveluAbstract:In a recently accepted paper of M. Ayub, H. Zaman and M. Ahmad [Cent. Eur. J. Phys. 8, 135 (2010)] the authors claim that the governing similarity equations of Vajravelu and Roper [Int. J. Nonlin. Mech. 34, 1031 (1999)] are incorrect; without any justification, the authors Ayub et al. simply mention that the equation is “found to be incorrect in the literature” (though no reference supporting this assertion is provided in the citations). We show that this assertion of Ayub et al. is wrong, and that the similarity equation of Vajravelu and Roper is indeed correct.
Robert A. Van Gorder - One of the best experts on this subject based on the ideXlab platform.
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Bounds, monotonicity, uniqueness, and analytical calculation of a class of similarity solutions for the fluid flow over a nonlinearly stretching sheet
Mathematical Methods in the Applied Sciences, 2014Co-Authors: Robert A. Van GorderAbstract:Invoking some estimates obtained in [F.T. Akyildiz et al., Mathematical Methods in the Applied Sciences 33 (2010) 601–606] (which presented an alternate method of proof for the present problem), we correct the parameter regime considered in [R.A. Van Gorder, K. Vajravelu, and F. T. Akyildiz, Existence and uniqueness results for a nonlinear differential equation arising in viscous flow over a nonlinearly stretching sheet, Applied Mathematics Letters 24 (2011) 238–242] and add some details, which were omitted in the original proof. After this is done, we formulate a more elegant method of proof, converting the nonlinear ODE into a first nonlinear order system. This gives us a more natural way to view the problem and lends insight into the behavior of the solutions. Finally, we give a new way to approximate the shooting parameter α = f ′ ′ (0) analytically, through minimization of the L2([0, ∞ )) norm of residual errors. This approximation demonstrates the behavior of the parameter α we expect from the proved theorems, as well as from numerical simulations. In this way, we obtain a concise analytical approximation to the similarity solution. In summary, from this analysis, we find that monotonicity of solutions and their derivatives is essential in determining uniqueness, and these monotone solutions can be approximated analytically in a fairly simple way. Copyright © 2014 John Wiley & Sons, Ltd.
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Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer
2013Co-Authors: Kuppalapalle Vajravelu, Robert A. Van GorderAbstract:Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems and often fail when used for problems with strong nonlinearity. Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering.Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA.
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Corrigendum to "Existence and uniqueness results for a nonlinear differential equation arising in MHD Falkner-Skan flow" [Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 2272-2277]
Communications in Nonlinear Science and Numerical Simulation, 2012Co-Authors: Robert A. Van Gorder, Kuppalapalle VajraveluAbstract:Abstract We correct the hypothesis for which the existence and uniqueness theorems of Van Gorder and Vajravelu [Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 2272–2277] hold. This correction modifies the range of parameters valid under the given theorems.
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Existence and uniqueness results for a nonlinear differential equation arising in viscous flow over a nonlinearly stretching sheet
Applied Mathematics Letters, 2011Co-Authors: Robert A. Van Gorder, Kuppalapalle Vajravelu, F. Talay AkyildizAbstract:Abstract We establish the existence and uniqueness results for a class of nonlinear third order ordinary differential equations arising in the viscous flow over a nonlinearly stretching sheet. In particular, we consider solutions over the semi-infinite interval [ 0 , ∞ ) . These results generalize the results of Vajravelu and Cannon [K. Vajravelu, J.R. Cannon, Applied Mathematics and Computation 181 (2006) 609], where they considered the finite interval [ 0 , R ] . Also in this paper, we answer their open question of finding the existence and uniqueness results for the problem over the semi-infinite domain and discuss the properties of the solution.
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Comment on “Series solution of hydromagnetic flow and heat transfer with hall effect in a second grade fluid over a stretching sheet”
Open Physics, 2010Co-Authors: Robert A. Van Gorder, Kuppalapalle VajraveluAbstract:In a recently accepted paper of M. Ayub, H. Zaman and M. Ahmad [Cent. Eur. J. Phys. 8, 135 (2010)] the authors claim that the governing similarity equations of Vajravelu and Roper [Int. J. Nonlin. Mech. 34, 1031 (1999)] are incorrect; without any justification, the authors Ayub et al. simply mention that the equation is “found to be incorrect in the literature” (though no reference supporting this assertion is provided in the citations). We show that this assertion of Ayub et al. is wrong, and that the similarity equation of Vajravelu and Roper is indeed correct.
P D Weidman - One of the best experts on this subject based on the ideXlab platform.
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comment on heat transfer in mhd viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non uniform heat source sink m m nandeppanavar k Vajravelu m s abel commun nonlinear sci numer simulat 16 2011 3578 3590
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: P D WeidmanAbstract:Abstract Two discrepancies are discovered in the paper of Nandeppanavar et al. (2011) [1] . First, the homogeneous solution for the temperature field is incorrect. Moreover, only one of the two homogeneous solutions that decay exponentially in the far field is presented; since two such solutions are available, a discussion of the selection process is needed. Second, the particular solution of the inhomogeneous energy equation is incorrect. These solutions are corrected and new tabulated results for the PST and PHF thermal problems are presented.
Patrick Weidman - One of the best experts on this subject based on the ideXlab platform.
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Comment on “Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink”, M.M. Nandeppanavar, K. Vajravelu & M.S. Abel [Commun Nonlinear Sci Numer Simulat 16 (2011) 3578–3590]
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: Patrick WeidmanAbstract:Abstract Two discrepancies are discovered in the paper of Nandeppanavar et al. (2011) [1] . First, the homogeneous solution for the temperature field is incorrect. Moreover, only one of the two homogeneous solutions that decay exponentially in the far field is presented; since two such solutions are available, a discussion of the selection process is needed. Second, the particular solution of the inhomogeneous energy equation is incorrect. These solutions are corrected and new tabulated results for the PST and PHF thermal problems are presented.
Hamed Shahmohamadi - One of the best experts on this subject based on the ideXlab platform.
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Reliable treatment of a new analytical method for solving MHD boundary-layer equations
Meccanica, 2010Co-Authors: Hamed ShahmohamadiAbstract:The purpose of this study is to implement a new analytical method which is a combination of the homotopy analysis method (HAM) and the Pade approximant for solving magnetohydrodynamic boundary-layer flow. The solution is compared with the numerical solution. Comparisons between the HAM–Pade and the numerical solution reveal that the new technique is a promising tool for solving MHD boundary-layer equations. The effects of the various parameters on the velocity and temperature profiles are presented graphically form. Favorable comparisons with previously published works (Crane, J. Appl. Math. Phys. 21:645–647, 1970, and Vajravelu and Hadjinicolaou, Int. J. Eng. Sci. 35:1237–1244, 1997) are obtained. It is predicted that HAM–Pade can have wide application in engineering problems (especially for boundary-layer and natural convection problems).
