Faculty Publications
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Item In this paper numerical methods for the initial value problems of general second order differential equations are derived. The methods depend upon the parameters p and q which are the new additional values of the coefficients of y? and y in the given differential equation. Here, we report a new two step fourth order method. As p tends to zero and q ? (2?/h)2 the method is absolutely stable. Numerical results are presented for Bessel's, Legendre's and general second order differential equations.(Elsevier, Additive parameters methods for the numerical integration of y? = f (t, y, y?)) Sesappa Rai, A.; Ananthakrishnaiah, U.1996Item A finite difference method assuming parabolic variation of contact pressure distribution is presented to obtain the influence lines for bending moments in beams on an elastic foundation. These influence lines can conveniently be used to find moments in beams on elastic foundations due to any type of loads. The computational procedure presented is simple. Accurate results are obtained with only 10 elements.(Elsevier Ltd, Influence lines for bending moments in beams on elastic foundations) Hosur, V.; Bhavikatti, S.S.1996Item A class of two-step implicit methods involving higher-order derivatives of y for initial value problems of the form y? = f(t, y, y?)is developed. The methods involve arbitrary parameters p and q, which are determined so that the methods become absolutely stable when applied to the test equation y? + ?y? + ?y = 0. Numerical results for Bessel's and general second-order differential equations are presented to illustrate that the methods are absolutely stable and are of order O(h4), O(h6) and O(h8).(Elsevier, Obrechkoff methods having additional parameters for general second-order differential equations) Sesappa Rai, A.; Ananthakrishnaiah, U.1997Item Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations(2011) Achar, S.D.In this paper, symmetric multistep Obrechkoff methods of orders 8 and 12, involving a parameter p to solve a special class of second order initial value problems in which the first order derivative does not appear explicitly, are discussed. It is shown that the methods have zero phase-lag when p is chosen as 2? times the frequency of the given initial value problem. © 2011 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 Vibration analysis of a tapered laminated thick composite plate with ply drop-offs(Springer Verlag service@springer.de, 2015) Edwin Sudhagar, P.; Arumugam, A.; Vasudevan, R.; Jeyaraj, J.In this study, vibration characteristics of a tapered laminated thick composite plate have been investigated using finite element method by including the shear deformation and rotary inertia effects. The governing differential equations of motion of a tapered laminated thick composite plate are presented in the finite element formulation based on first-order shear deformation theory for three types of taper configurations. The effectiveness of the developed finite element formulation in identifying the various dynamic properties of a tapered laminated thick composite plate is demonstrated by comparing natural frequencies evaluated using the present FEM with those obtained from the experimental measurements and presented in the available literature. Various parametric studies are also performed to investigate the effect of taper configurations, aspect ratio, taper angle, angle ply orientation and boundary conditions on free and forced vibration responses of the structures. The comparison of the transverse free vibration mode shapes of the uniform and tapered composite plates under various boundary conditions is also presented. The forced vibration response of a composite plate is investigated to study the dynamic response of tapered composite plate under the harmonic force excitation in various tapered configurations. It is concluded that the dynamic properties of laminated thick composite plates could be tailored by dropping off the plies to yield various tapered composite plate. © 2015, Springer-Verlag Berlin Heidelberg.Item Analysis of cortical rhythms in intracranial EEG by temporal difference operators during epileptic seizures(Elsevier Ltd, 2016) Malali, A.; Chaitanya, G.; Gowda, S.; Majumdar, K.Brain oscillations have traditionally been studied by time-frequency analysis of the electrophysiological signals. In this work we demonstrated the usefulness of two nonlinear combinations of differential operators on intracranial EEG (iEEG) recordings to study abnormal oscillations in human brain during intractable focal epileptic seizures. Each one dimensional time domain signal was visualized as the trajectory of a particle moving in a force field with one degree of freedom. Modeling of the temporal difference operators to be applied on the signals was inspired by the principles of classical Newtonian mechanics. Efficiency of one of the nonlinear combinations of the operators in distinguishing the seizure part from the background signal and the artifacts was established, particularly when the seizure duration was long. The resultant automatic detection algorithm is linear time executable and detects a seizure with an average delay of 5.02 s after the electrographic onset, with a mean 0.05/h false positive rate and 94% detection accuracy. The area under the ROC curve was 0.959. Another nonlinear combination of differential operators detects spikes (peaks) and inverted spikes (troughs) in a signal irrespective of their shape and size. It was shown that in a majority of the cases simultaneous occurrence of all the spikes and inverted spikes across the focal channels was more after the seizure offset than during the seizure, where the duration after the offset was taken equal to the duration of the seizure. It has been explained in terms of GABAergic inhibition of seizure termination. © 2016 Elsevier Ltd. All rights reserved.Item Structural optimization of rotating tapered laminated thick composite plates with ply drop-offs(Springer Netherlands, 2017) Edwin Sudhagar, P.; Arumugam, A.; Vasudevan, V.; Jeyaraj, J.In this study, structural optimization of rotating tapered thick laminated composite plates with ply drop-offs has been investigated numerically. The governing differential equations of motion of the tapered composite plate have been presented including the energy associated with the inertia force, coriolis force, displacement dependent centrifugal force and initial stress resultants due to steady state rotation. Four noded quadrilateral finite element has been formulated based on the first order shear deformation theory. Finite element analysis results are validated with experimental results for natural frequencies of the tapered plate with various configurations. Various cases of optimization problems are formulated with different objective functions in terms of maximization of natural frequencies and damping factors (individually and combined) and solved using genetic algorithm in order to obtain optimal ply sequence and ply orientation. It is shown that the optimization problem with maximization of fundamental modal damping factor without rotating condition yields the optimal layout as 90° for all the layers in the plate. It is also observed that maximization of the fundamental modal damping factor yields identical optimal orientation for uniform and all the configurations of a tapered composite plate. © 2015, Springer Science+Business Media Dordrecht.Item Euclidean thermodynamics and Lyapunov exponents of Einstein–Power–Yang–Mills AdS black holes(Springer Nature, 2025) Karthik, R.; Dillirajan, D.; Ajith, K.M.; Hegde, K.; Punacha, S.; Naveena Kumara, A.N.We study the thermodynamics of Einstein–Power–Yang–Mills AdS black holes via the Euclidean path integral method, incorporating appropriate boundary and counterterms. By analyzing unstable timelike and null circular geodesics, we demonstrate that their Lyapunov exponents reflect the thermodynamic phase structure obtained from the Euclidean action. Specifically, the small-large black hole phase transition, analogous to a van der Waals fluid, is signaled by a discontinuity in the Lyapunov exponent. Treating this discontinuity as an order parameter, we observe a universal critical exponent of 1/2, consistent with mean-field theory. These results extend previous insights from black hole spacetimes with Abelian charges to scenarios involving nonlinear, non-Abelian gauge fields, highlighting the interplay between black hole thermodynamics and chaotic dynamics. © The Author(s) 2025.