Faculty Publications
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Item Densities and viscosities of poly(ethylene glycol) 4000 + diammonium hydrogen phosphate + water systems(2009) Iyyaswami, I.; Murugesan, S.; Amaresh, S.P.; Govindarajan, R.; Murugesan, T.The densities and viscosities of binary and ternary solutions of the poly(ethylene glycol) 4000 (PEG4000) + diammonium hydrogen phosphate + water system were determined at different temperatures [(298.15, 303.15, 308.15, 313.15, and 318.15) K]. The measured density and viscosity data of all the binary and ternary systems were fitted to available empirical correlations, for the corresponding temperatures. The density data show a linear variation with mass fraction of the polymer for all temperatures. The viscosity data of all the solutions were correlated as a function of their mass fraction, using a nonlinear equation, for the five different temperatures covered in the present work. Densities and viscosities of PEG4000 - diammonium hydrogen phosphate two-phase systems have been measured at (298.15, 303.15, 308.15, 313.15, and 318.15) K. The tie line lengths (TLL) of the aqueous two-phase systems have also been estimated, and the effect of the physical properties on the TLL is also reported. © 2009 American Chemical Society.Item A quadratic convergence yielding iterative method for nonlinear ill-posed operator equations(2012) George, S.; Elmahdy, A.I.In this paper, we consider an iterative method for the approximate solution of the nonlinear ill-posed operator equation Tx = y; where the right hand side is replaced by noisy data y? ? X with ?y - y ?? ? ? and T : D(T) ? X ? X is a nonlinear monotone operator defined on a Hilbert space X: The iteration x ?n,? converges quadratically to the unique solution x?? of the equation T(x) + ?(x - x0) = y? (x0 := x 0,??). It is known that (Tautanhahn (2002)) x?? converges to the solution x? of Tx = y: The convergence analysis and the stopping rule are based on a suitably constructed majorizing sequence. Under a general source condition on x 0 - x? we proved that the error ?x? - x n, ??;? is of optimal order. We show that the adaptive scheme considered by Perverzev and Schock (2005) for choosing the regularization parameter can be effectively used here for obtaining an optimal order error estimate. © 2012 Institute of Mathematics, NAS of Belarus.Item An application of newton type iterative method for lavrentiev regularization for ill-posed equations: Finite dimensional realization(2012) George, S.; Pareth, S.In this paper, we consider, a finite dimensional realization of Newton type iterative method for Lavrentiev regularization of ill-posed equations. Precisely we consider the ill-posed equation F(x) = f when the available data is f ? withItem Expanding the applicability of Tikhonov's regularization and iterative approximation for ill-posed problems(Walter de Gruyter GmbH, 2014) Vasin, V.; George, S.Recently, Vasin [J. Inverse Ill-Posed Probl. 21 (2013), 109-123] considered a new iterative method for approximately solving nonlinear ill-posed operator equation in Hilbert spaces. In this paper we introduce a modified form of the method considered by Vasin. This paper weakens the conditions needed in the existing results. We use a center-type Lipschitz condition in our convergence analysis instead of a Lipschitz-type condition used in [J. Inverse Ill-Posed Probl. 21 (2013), 109-123]. This way a tighter convergence analysis is obtained and under less computational cost, since the more precise and easier to compute center-Lipschitz instead of the Lipschitz constant is used in the convergence analysis. Order optimal error bounds are given in case the regularization parameter is chosen a priori and by the adaptive method of Pereverzev and Schock [SIAM J. Numer. Anal. 43 (2005), 2060-2076]. A numerical example of a nonlinear integral equation proves the efficiency of the proposed method. © 2014 by De Gruyter.Item A quadratic convergence yielding iterative method for the implementation of Lavrentiev regularization method for ill-posed equations(Elsevier Inc. usjcs@elsevier.com, 2015) Padikkal, P.; Shubha, V.S.; George, S.George and Elmahdy (2012), considered an iterative method which converges quadratically to the unique solution x?? of the method of Lavrentiev regularization, i.e., F(x) + ?(x - x0) = y?, approximating the solution x of the ill-posed problem F(x) = y where F:D(F)?X?X is a nonlinear monotone operator defined on a real Hilbert space X. The convergence analysis of the method was based on a majorizing sequence. In this paper we are concerned with the problem of expanding the applicability of the method considered by George and Elmahdy (2012) by weakening the restrictive conditions imposed on the radius of the convergence ball and also by weakening the popular Lipschitz-type hypotheses considered in earlier studies such as George and Elmahdy (2012), Mahale and Nair (2009), Mathe and Perverzev (2003), Nair and Ravishankar (2008), Semenova (2010) and Tautanhahn (2002). We show that the adaptive scheme considered by Perverzev and Schock (2005) for choosing the regularization parameter can be effectively used here for obtaining order optimal error estimate. In the concluding section the method is applied to numerical solution of the inverse gravimetry problem. © 2014 Elsevier Inc. All rights reserved.Item A modified quasilinearization method for fractional differential equations and its applications(Elsevier Inc. usjcs@elsevier.com, 2015) Vijesh, V.; Roy, R.; Godavarma, G.Abstract In this paper, we prove an existence and uniqueness theorem for solving the nonlinear fractional differential equation of Caputo's type of order q ? (0, 1] using the method of modified quasilinearization. The main theorem has been illustrated numerically using appropriate examples which shows that the proposed quasilinearization method is robust and easy to apply. © 2015 Elsevier Inc.Item Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative(Elsevier Inc. usjcs@elsevier.com, 2015) Argyros, I.K.; George, S.Abstract We present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for these methods under hypotheses only on the first Fréchet derivative in contrast to earlier studies such as Adomian (1994) [1], Babajee et al. (2008) [13], Cordero and Torregrosa (2007) [17], Cordero et al. [18], Darvishi and Barati (2007) [19], using hypotheses reaching up to the fourth Fréchet derivative although only the first derivative appears in these methods. This way we expand the applicability of these methods. Numerical examples are also presented in this study. © 2015 Elsevier Inc.Item Finite dimensional realization of a quadratic convergence yielding iterative regularization method for ill-posed equations with monotone operators(Elsevier Inc. usjcs@elsevier.com, 2016) Shubha, V.S.; George, S.; Padikkal, P.; Erappa, M.E.Recently Jidesh et al. (2015), considered a quadratic convergence yielding iterative method for obtaining approximate solution to nonlinear ill-posed operator equation F(x)=y, where F: D(F) ? X ? X is a monotone operator and X is a real Hilbert space. In this paper we consider the finite dimensional realization of the method considered in Jidesh et al. (2015). Numerical example justifies our theoretical results. © 2015 Elsevier Inc. All rights reserved.Item Squeeze casting process modeling by a conventional statistical regression analysis approach(Elsevier Inc. usjcs@elsevier.com, 2016) Gowdru Chandrashekarappa, G.C.; Krishna, P.; Parappagoudar, M.B.During the casting process, the alloy composition, melt treatment modification, processing method, and process variables change the microstructure, thereby affecting the mechanical properties. The hybrid squeeze casting method has been used to limit casting defects, refine the micro-structure, and enhance the mechanical properties. The process variables influence the mechanical and micro-structure properties during squeeze casting. In the present study, we established nonlinear input–output relationships and explored the physical behavior of this process based on the statistical design of experiments and using the response surface methodology. Experiments were conducted to measure the responses in terms of the density, hardness, and secondary dendrite arm spacing. Two nonlinear regression models, i.e., Box–Behnken design and central composite design, were used to conduct experiments, collect experimental data, identify significant process variables, analyze the collected data, and establish the complex input–output relationships. Surface plots were used to explore the effects of the squeeze pressure, pressure duration, pouring, and die temperature on the measured responses. Analysis of variance tests were conducted to evaluate the statistical suitability of the models developed. Furthermore, the accuracies of the predictions made by the models were investigated based on test cases. We found that both of the nonlinear models were statistically adequate and they provided complete insights into the complex nonlinear input–output relationships. Central composite design performed better for the secondary dendrite arm spacing and hardness responses, whereas its performance was the same as that of Box–Behnken design for the density response. The relationships between the responses (i.e., outputs) were established by generating large volumes of input–output data using the nonlinear regression models. We found that the density, hardness, and secondary dendrite arm spacing responses could be obtained by utilizing the nonlinear regression equations and the same set of process variables. Furthermore, the secondary dendrite arm spacing response could be expressed as third order nonlinear functions of density or hardness (structure to property relationship). The results showed that the secondary dendrite arm spacing had inverse relationships with density and hardness, whereas density and hardness had direct relationships. © 2016 Elsevier LtdItem Ball convergence of a sixth order iterative method with one parameter for solving equations under weak conditions(Springer-Verlag Italia s.r.l., 2016) Argyros, I.K.; George, S.We present a local convergence analysis of a sixth order iterative method for approximate a locally unique solution of an equation defined on the real line. Earlier studies such as Sharma et al. (Appl Math Comput 190:111–115, 2007) have shown convergence of these methods under hypotheses up to the fifth derivative of the function although only the first derivative appears in the method. In this study we expand the applicability of these methods using only hypotheses up to the first derivative of the function. Numerical examples are also presented in this study. © 2015, Springer-Verlag Italia.