International Journal of Engineering Mathematics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Effects of Temperature and Stirring on Mass Transfer to Maximize Biodiesel Production from Jatropha curcas Oil: A Mathematical Study Tue, 27 Oct 2015 14:02:39 +0000 Biodiesel, the most promising renewable and alternative energy, is produced through transesterification of vegetable oils. One of the most cost effective sources of biodiesel is Jatropha curcas oil. Transesterification of Jatropha oil depends significantly on reaction parameters such as reaction time, temperature, molar ratio, catalyst amount, and stirrer speed. Among these parameters temperature and stirring have noteworthy effect on mass transfer. In this research article, we have shown the simultaneous effect of temperature and stirring on mass transfer by considering a mathematical model. The optimal profiles of temperature and stirring are determined as a combined parameter, for which maximum biodiesel can be obtained. Further, we have shown that this pair exists and is unique for the optimality of the system. Fahad Al Basir and Priti Kumar Roy Copyright © 2015 Fahad Al Basir and Priti Kumar Roy. All rights reserved. Successive Complementary Expansion Method for Solving Troesch’s Problem as a Singular Perturbation Problem Tue, 27 Oct 2015 06:32:42 +0000 A simple and efficient method that is called Successive Complementary Expansion Method (SCEM) is applied for approximation to an unstable two-point boundary value problem which is known as Troesch’s problem. In this approach, Troesch’s problem is considered as a singular perturbation problem. We convert the hyperbolic-type nonlinearity into a polynomial-type nonlinearity using an appropriate transformation, and then we use a basic zoom transformation for the boundary layer and finally obtain a nonlinear ordinary differential equation that contains SCEM complementary approximation. We see that SCEM gives highly accurate approximations to the solution of Troesch’s problem for various parameter values. Moreover, the results are compared with Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM) by using tables. Süleyman Cengizci and Aytekin Eryılmaz Copyright © 2015 Süleyman Cengizci and Aytekin Eryılmaz. All rights reserved. An Efficient Method to Find Solutions for Transcendental Equations with Several Roots Thu, 15 Oct 2015 13:06:26 +0000 This paper presents a method for obtaining a solution for all the roots of a transcendental equation within a bounded region by finding a polynomial equation with the same roots as the transcendental equation. The proposed method is developed using Cauchy’s integral theorem for complex variables and transforms the problem of finding the roots of a transcendental equation into an equivalent problem of finding roots of a polynomial equation with exactly the same roots. The interesting result is that the coefficients of the polynomial form a vector which lies in the null space of a Hankel matrix made up of the Fourier series coefficients of the inverse of the original transcendental equation. Then the explicit solution can be readily obtained using the complex fast Fourier transform. To conclude, the authors present an example by solving for the first three eigenvalues of the 1D transient heat conduction problem. Rogelio Luck, Gregory J. Zdaniuk, and Heejin Cho Copyright © 2015 Rogelio Luck et al. All rights reserved. Mixed Convection Flow of Magnetic Viscoelastic Polymer from a Nonisothermal Wedge with Biot Number Effects Mon, 12 Oct 2015 12:55:18 +0000 Magnetic polymers are finding increasing applications in diverse fields of chemical and mechanical engineering. In this paper, we investigate the nonlinear steady boundary layer flow and heat transfer of such fluids from a nonisothermal wedge. The incompressible Eyring-Powell non-Newtonian fluid model is employed and a magnetohydrodynamic body force is included in the simulation. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, the Eyring-Powell rheological fluid parameter (), local non-Newtonian parameter based on length scale (), Prandtl number (Pr), Biot number (), pressure gradient parameter (), magnetic parameter (), mixed convection parameter (), and dimensionless tangential coordinate (), on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. S. Abdul Gaffar, V. Ramachandra Prasad, Bhuvana Vijaya, and O. Anwar Beg Copyright © 2015 S. Abdul Gaffar et al. All rights reserved. Robust Adaptive Exponential Synchronization of Two Different Stochastic Perturbed Chaotic Systems with Structural Perturbations Tue, 29 Sep 2015 07:49:15 +0000 The robust adaptive exponential synchronization problem of stochastic chaotic systems with structural perturbations is investigated in mean square. The stochastic disturbances are assumed to be Brownian motions that act on the slave system and the norm-bounded uncertainties exist in all parameters after decoupling. The stochastic disturbances could reflect more realistic dynamical behaviors of the coupled chaotic system presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques, and adaptive control laws, we derive several sufficient conditions that ensure the coupled chaotic systems to be robustly exponentially synchronized in the mean square for all admissible parameter uncertainties. This approach cannot only make the outputs of both master and slave systems reach synchronization with the passage of time between both systems but also attenuate the effects of the perturbation on the overall error system to a prescribed level. The main results are shown to be general enough to cover many existing ones reported in the literature. A. Soup Tewa Kammogne and H. B. Fotsin Copyright © 2015 A. Soup Tewa Kammogne and H. B. Fotsin. All rights reserved. Block Backward Differentiation Formulas for Fractional Differential Equations Tue, 29 Sep 2015 07:39:16 +0000 This paper concerns the numerical approximation of Fractional Initial Value Problems (FIVPs). This is achieved by constructing -step continuous BDFs. These continuous schemes are developed via the interpolation and collocation approach and are used to obtain the discrete -step BDF and () additional methods which are applied as numerical integrators in a block-by-block mode for the integration of FIVP. The properties of the methods are established and regions of absolute stability of the methods are plotted in the complex plane. Numerical tests including large systems arising form the semidiscretization of one-dimensional fractional Burger’s equation show that the methods are highly accurate and efficient. T. A. Biala and S. N. Jator Copyright © 2015 T. A. Biala and S. N. Jator. All rights reserved. Homotopy Simulation of Nonlinear Unsteady Rotating Nanofluid Flow from a Spinning Body Sun, 27 Sep 2015 09:04:28 +0000 The development of new applications of nanofluids in chemical engineering and other technologies has stimulated significant interest in computational simulations. Motivated by coating applications of nanomaterials, we investigate the transient nanofluid flow from a time-dependent spinning sphere using laminar boundary layer theory. The free stream velocity varies continuously with time. The unsteady conservations equations are normalized with appropriate similarity transformations and rendered into a ninth-order system of nonlinear coupled, multidegree ordinary differential equations. The transformed nonlinear boundary value problem is solved using the homotopy analysis method (HAM), a semicomputational procedure achieving fast convergence. Computations are verified with an Adomian decomposition method (ADM). The influence of acceleration parameter, rotational body force parameter, Brownian motion number, thermophoresis number, Lewis number, and Prandtl number on surface shear stress, heat, and mass (nanoparticle volume fraction) transfer rates is evaluated. The influence on boundary layer behavior is also investigated. HAM demonstrates excellent stability and leads to highly accurate solutions. O. Anwar Bég, F. Mabood, and M. Nazrul Islam Copyright © 2015 O. Anwar Bég et al. All rights reserved. Improving the Performance of Metaheuristics: An Approach Combining Response Surface Methodology and Racing Algorithms Wed, 16 Sep 2015 09:36:25 +0000 The setup of heuristics and metaheuristics, that is, the fine-tuning of their parameters, exercises a great influence in both the solution process, and in the quality of results of optimization problems. The search for the best fit of these algorithms is an important task and a major research challenge in the field of metaheuristics. The fine-tuning process requires a robust statistical approach, in order to aid in the process understanding and also in the effective settings, as well as an efficient algorithm which can summarize the search process. This paper aims to present an approach combining design of experiments (DOE) techniques and racing algorithms to improve the performance of different algorithms to solve classical optimization problems. The results comparison considering the default metaheuristics and ones using the settings suggested by the fine-tuning procedure will be presented. Broadly, the statistical results suggest that the fine-tuning process improves the quality of solutions for different instances of the studied problems. Therefore, by means of this study it can be concluded that the use of DOE techniques combined with racing algorithms may be a promising and powerful tool to assist in the investigation, and in the fine-tuning of different algorithms. However, additional studies must be conducted to verify the effectiveness of the proposed methodology. Eduardo Batista de Moraes Barbosa, Edson Luiz França Senne, and Messias Borges Silva Copyright © 2015 Eduardo Batista de Moraes Barbosa et al. All rights reserved. Rational-Like Solutions of a Differential-Difference Equation Related to Ablowitz-Ladik Spectral Problem Thu, 03 Sep 2015 14:00:43 +0000 By using the Casoratian technique, we construct the double Casoratian solutions whose entries satisfy matrix equation of a differential-difference equation related to the Ablowitz-Ladik spectral problem. Soliton solutions and rational-like solutions are obtained from taking special cases in general solutions. Jiang-ping Zhang, Qi Li, and Shou-ting Chen Copyright © 2015 Jiang-ping Zhang et al. All rights reserved. A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics Mon, 31 Aug 2015 13:00:10 +0000 The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order , using wavelets. The philosophy behind the proposed algorithm is to replace the part of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing as a Fourier-Bessel series with coefficients depending strongly on the input function . The wavelet method indicates that the approach is easy to implement and thus computationally very attractive. Nagma Irfan and A. H. Siddiqi Copyright © 2015 Nagma Irfan and A. H. Siddiqi. All rights reserved. Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence Sun, 07 Dec 2014 07:38:14 +0000 In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result. Amine Bernoussi, Abdelilah Kaddar, and Said Asserda Copyright © 2014 Amine Bernoussi et al. All rights reserved. Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary Condition Thu, 06 Nov 2014 12:43:54 +0000 An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement. N. Bhaskar Reddy, T. Poornima, and P. Sreenivasulu Copyright © 2014 N. Bhaskar Reddy et al. All rights reserved. Aligned Magnetic Field, Radiation, and Rotation Effects on Unsteady Hydromagnetic Free Convection Flow Past an Impulsively Moving Vertical Plate in a Porous Medium Tue, 21 Oct 2014 09:06:38 +0000 We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases. Sandeep Naramgari, Sugunamma Vangala, and Mohankrishna Penem Copyright © 2014 Sandeep Naramgari et al. All rights reserved. Quadratic Prediction Models for the Performance Comparison of a Marine Engine Fuelled with Biodiesels B5 and B20 Tue, 30 Sep 2014 08:34:28 +0000 According to Thailand’s renewable energy development plan, biodiesel is one of the interesting alternative energies. In this research, biodiesels B5 and B20 are tested in a marine engine. The experimental results are then compared by using three different techniques including (1) the conventional technique, (2) average of the point-to-point comparisons, and (3) a comparison by using quadratic prediction models. This research aims to present the procedures of these techniques in-depth. The results show that the comparison by using quadratic prediction models can accurately predict ample amounts of results and make the comparison more logical. The results are compatible with those of the conventional technique, while the average of the point-to-point comparisons shows diverse results. These results are also explained on the fuel property basis, confirming that the quadratic prediction model and the conventional technique are practical, but the average of the point-to-point comparison technique presents an inaccurate result. The benefit of this research shows that the quadratic prediction model is more flexible for future science and engineering experimental design, thus reducing cost and time usage. The details of the calculation, results, and discussion are presented in the paper. Chedthawut Poompipatpong Copyright © 2014 Chedthawut Poompipatpong. All rights reserved. A New Approach to Solve Intuitionistic Fuzzy Optimization Problem Using Possibility, Necessity, and Credibility Measures Thu, 25 Sep 2014 13:03:03 +0000 Corresponding to chance constraints, real-life possibility, necessity, and credibility measures on intuitionistic fuzzy set are defined. For the first time the mathematical and graphical representations of different types of measures in trapezoidal intuitionistic fuzzy environment are defined in this paper. We have developed intuitionistic fuzzy chance constraints model (CCM) based on possibility and necessity measures. We have also proposed a new method for solving an intuitionistic fuzzy CCM using chance operators. To validate the proposed method, we have discussed three different approaches to solve the intuitionistic fuzzy linear programming (IFLPP) using possibility, necessity and credibility measures. Numerical and graphical representations of optimal solutions of the given example at different possibility and necessity, levels have been discussed. Dipankar Chakraborty, Dipak Kumar Jana, and Tapan Kumar Roy Copyright © 2014 Dipankar Chakraborty et al. All rights reserved. Design of Robust Output Feedback Guaranteed Cost Control for a Class of Nonlinear Discrete-Time Systems Wed, 10 Sep 2014 09:40:54 +0000 This paper investigates static output feedback guaranteed cost control for a class of nonlinear discrete-time systems where the delay in state vector is inconsistent with the delay in nonlinear perturbations. Based on the output measurement, the controller is designed to ensure the robust exponentially stability of the closed-loop system and guarantee the performance of system to achieve an adequate level. By using the Lyapunov-Krasovskii functional method, some sufficient conditions for the existence of robust output feedback guaranteed cost controller are established in terms of linear matrix inequality. A numerical example is provided to show the effectiveness of the results obtained. Yan Zhang, Yali Dong, and Tianrui Li Copyright © 2014 Yan Zhang et al. All rights reserved. Numerical Analysis of Vibration Isolation Using Pile Rows against the Vibration due to Moving Loads in a Viscoelastic Medium Mon, 08 Sep 2014 05:29:45 +0000 A numerical method for evaluating the vertical vibration isolation effect of pile rows embedded in a viscoelastic half space subjected to a moving load is developed in this paper on the basis of the Cole-Cole model and Muki’s method. Based on the proposed method, the influence of various parameters on the vibration isolation effect of pile rows embedded in the viscoelastic half space is investigated numerically. Bin Xu and Man-Qing Xu Copyright © 2014 Bin Xu and Man-Qing Xu. All rights reserved. A Modified Strip-Yield-Saturation-Induction Model Solution for Cracked Piezoelectromagnetic Plate Thu, 14 Aug 2014 00:00:00 +0000 A strip-yield-saturation-induction model is proposed for an impermeable crack embedded in piezoelectromagnetic plate. The developed slide-yield, saturation, and induction zones are arrested by distributing, respectively, mechanical, electrical, and magnetic loads over their rims. Two cases are considered: when saturation zone exceeds induction zone and vice-versa. It is assumed that developed slide-yield zone is the smallest because of the brittle nature of piezoelectromagnetic material. Fourier integral transform technique is employed to obtain the solution. Closed form analytic expressions are derived for developed zones lengths, crack sliding displacement, crack opening potential drop, crack opening induction drop, and energy release rate. Case study presented for BaTiO3–CoFe2O4 shows that crack arrest is possible under small-scale mechanical, electrical, and magnetic yielding. R. R. Bhargava and Pooja Raj Verma Copyright © 2014 R. R. Bhargava and Pooja Raj Verma. All rights reserved. Inviscid Uniform Shear Flow past a Smooth Concave Body Wed, 23 Jul 2014 00:00:00 +0000 Uniform shear flow of an incompressible inviscid fluid past a two-dimensional smooth concave body is studied; a stream function for resulting flow is obtained. Results for the same flow past a circular cylinder or a circular arc or a kidney-shaped body are presented as special cases of the main result. Also, a stream function for resulting flow around the same body is presented for an oncoming flow which is the combination of a uniform stream and a uniform shear flow. Possible fields of applications of this study include water flows past river islands, the shapes of which deviate from circular or elliptical shape and have a concave region, or past circular arc-shaped river islands and air flows past concave or circular arc-shaped obstacles near the ground. Abdullah Murad Copyright © 2014 Abdullah Murad. All rights reserved. Process Parameter Identification in Thin Film Flows Driven by a Stretching Surface Mon, 21 Jul 2014 10:30:31 +0000 The flow of a thin liquid film over a heated stretching surface is considered in this study. Due to a potential nonuniform temperature distribution on the stretching sheet, a temperature gradient occurs in the fluid which produces surface tension gradient at the free surface of the thin film. As a result, the free surface deforms and these deformations are advected by the flow in the stretching direction. This work focuses on the inverse problem of reconstructing the sheet temperature distribution and the sheet stretch rate from observed free surface variations. This work builds on the analysis of Santra and Dandapat (2009) who, based on the long-wave expansion of the Navier-Stokes equations, formulate a partial differential equation which describes the evolution of the thickness of a film over a nonisothermal stretched surface. In this work, we show that after algebraic manipulation of a discrete form of the governing equations, it is possible to reconstruct either the unknown temperature field on the sheet and hence the resulting heat transfer or the stretching rate of the underlying surface. We illustrate the proposed methodology and test its applicability on a range of test problems. Satyananda Panda, Mathieu Sellier, M. C. S. Fernando, and M. K. Abeyratne Copyright © 2014 Satyananda Panda et al. All rights reserved. Weak Nonlinear Double-Diffusive Magnetoconvection in a Newtonian Liquid under Temperature Modulation Sun, 06 Jul 2014 12:09:11 +0000 The present paper deals with a weak nonlinear theory of double-diffusive magnetoconvection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to imposed time-periodic thermal boundaries. The temperature of both walls is varied time periodic in this case. The disturbances are expanded in terms of power series of amplitude of convection, which is assumed to be small. Using nonautonomous Ginzburg-Landau equation, the Nusselt and Sherwood numbers obtained analytically and studied heat and mass transport in the system. Effect of various parameters on the heat and mass transport is discussed extensively. It is found that the effect of magnetic field is to stabilize the system. Further, it is also notified that the heat and mass transport can be controlled by suitably adjusting the external parameters of the system. B. S. Bhadauria and Palle Kiran Copyright © 2014 B. S. Bhadauria and Palle Kiran. All rights reserved. Jeffrey Fluid Flow through Porous Medium in the Presence of Magnetic Field in Narrow Tubes Wed, 25 Jun 2014 09:24:41 +0000 Jeffrey fluid flow in the presence of magnetic field through porous medium in tubes of small diameters is studied. It is assumed that the core region consists of a Jeffrey fluid and the peripheral region of a Newtonian fluid. Making the assumptions as in the work of Chaturani and Upadhya, the linearised equations of motion have been solved and analytical solution has been obtained. The influence of various pertinent parameters on the flow characteristics such as effective viscosity, core hematocrit, and mean hematocrit has been studied and discussed through graphs. It is found that the effective viscosity and mean hematocrit decrease with Jeffrey parameter and Darcy number but increase with tube hematocrit and tube radius. Also, the core hematocrit decreases with Jeffrey parameter, Darcy number, tube hematocrit, and tube radius. Further, it is noticed that the flow exhibits the anomalous Fahraeus-Lindquist effect. Santhosh Nallapu and G. Radhakrishnamacharya Copyright © 2014 Santhosh Nallapu and G. Radhakrishnamacharya. All rights reserved. Analytical Solutions of Some Fully Developed Flows of Couple Stress Fluid between Concentric Cylinders with Slip Boundary Conditions Tue, 17 Jun 2014 06:26:41 +0000 We establish, in this paper, the closed form analytical solutions of steady fully developed flows of couple stress fluid between two concentric cylinders, generated due to the constant pressure gradient or the translatory motion of the outer cylinder or both, using the slip boundary conditions. The classical solutions for Newtonian fluid in the hydrodynamic case appear as a limiting case of our solutions. The velocity profiles of the flows are presented and the effect of various parameters on velocity is discussed. The results indicate that the presence of couple stresses decreases the velocity of the fluid. M. Devakar, D. Sreenivasu, and B. Shankar Copyright © 2014 M. Devakar et al. All rights reserved. Inversion of Fourier Transforms by Means of Scale-Frequency Series Tue, 27 May 2014 00:00:00 +0000 We report on inversion of the Fourier transform when the frequency variable can be scaled in a variety of different ways that improve the resolution of certain parts of the frequency domain. The corresponding inverse Fourier transform is shown to exist in the form of two dual scale-frequency series. Upon discretization of the continuous scale factor, this Fourier transform series inverse becomes a certain nonharmonic double series, a discretized scale-frequency (DSF) series. The DSF series is also demonstrated, theoretically and practically, to be rate-optimizable with respect to its two free parameters, when it satisfies, as an entropy maximizer, a pertaining recursive nonlinear programming problem incorporating the entropy-based uncertainty principle. Nassar H. S. Haidar Copyright © 2014 Nassar H. S. Haidar. All rights reserved. Controller Design for an Observer-Based Modified Repetitive-Control System Tue, 13 May 2014 11:33:54 +0000 This paper presents a method of designing a state-observer based modified repetitive-control system that provides a given level of disturbance attenuation for a class of strictly proper linear plants. Since the time delay in a repetitive controller can be treated as a kind of disturbance, we convert the system design problem into a standard state-feedback control problem for a linear time-invariant system. The Lyapunov functional and the singular-value decomposition of the output matrix are used to derive a linear-matrix-inequality (LMI) based design algorithm for the parameters of the feedback controller and the state-observer. A numerical example demonstrates the validity of the method. Lan Zhou, Jinhua She, Shaowu Zhou, and Qiwei Chen Copyright © 2014 Lan Zhou et al. All rights reserved. An Application of Filtered Renewal Processes in Hydrology Mon, 05 May 2014 07:58:36 +0000 Filtered renewal processes are used to forecast daily river flows. For these processes, contrary to filtered Poisson processes, the time between consecutive events is not necessarily exponentially distributed, which is more realistic. The model is applied to obtain one- and two-day-ahead forecasts of the flows of the Delaware and Hudson Rivers, both located in the United States. Better results are obtained than with filtered Poisson processes, which are often used to model river flows. Mario Lefebvre and Fatima Bensalma Copyright © 2014 Mario Lefebvre and Fatima Bensalma. All rights reserved. Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell Mon, 28 Apr 2014 00:00:00 +0000 This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease. Rajitha Gurijala and Malla Reddy Perati Copyright © 2014 Rajitha Gurijala and Malla Reddy Perati. All rights reserved. On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions Tue, 01 Apr 2014 07:21:21 +0000 The th-order nonlinearity of Boolean function plays a central role against several known attacks on stream and block ciphers. Because of the fact that its maximum equals the covering radius of the th-order Reed-Muller code, it also plays an important role in coding theory. The computation of exact value or high lower bound on the th-order nonlinearity of a Boolean function is very complicated problem, especially when . This paper is concerned with the computation of the lower bounds for third-order nonlinearities of two classes of Boolean functions of the form for all , , where , where , , and are integers such that and , and , where is a positive integer such that and . Brajesh Kumar Singh Copyright © 2014 Brajesh Kumar Singh. All rights reserved. Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions Mon, 24 Feb 2014 11:54:01 +0000 Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme. Ishfaq Ahmad Ganaie, Shelly Arora, and V. K. Kukreja Copyright © 2014 Ishfaq Ahmad Ganaie et al. All rights reserved. Several New Third-Order and Fourth-Order Iterative Methods for Solving Nonlinear Equations Sun, 23 Feb 2014 09:20:23 +0000 In order to find the zeros of nonlinear equations, in this paper, we propose a family of third-order and optimal fourth-order iterative methods. We have also obtained some particular cases of these methods. These methods are constructed through weight function concept. The multivariate case of these methods has also been discussed. The numerical results show that the proposed methods are more efficient than some existing third- and fourth-order methods. Anuradha Singh and J. P. Jaiswal Copyright © 2014 Anuradha Singh and J. P. Jaiswal. All rights reserved.