Journal of Advances in Applied Mathematics

8

Authors: Sangeeta Kumari, Baljeet Singh

Lord and Shulman theory of generalized thermoelasticity is applied to formulate the field equations governing a two-temperature thermoelastic medium with diffusion. The equations are reduced for an isotropic case in x-z plane. These equations are solved for general surface wave solutions. Particular solutions satisfying the required radiations conditions are obtained in a half-space. Applying suitable boundary conditions at free surface, a secular equation for wave speed of Rayleigh surface wave is obtained. The wave speed of Rayleigh wave is computed by using Fortran Program of iteration method for a particular example of the half-space. The effects of two-temperature parameter, frequency, thermodiffusion parameter and diffusion relaxation time are observed graphically on the wave speed of Rayleigh wave.

11

Authors: Harmanpreet Singh Kapoor, Kanchan Jain, Suresh Kumar Sharma

The widely used Generalized Additive Model (GAM) is a flexible and effective technique for conducting non-linear regression analysis. It relaxes the usual parametric assumptions and enables us to uncover structure in the relationship between the independent and dependent variable in exponential family that might be otherwise missed. In this paper, we describe the use of GAM procedure to determine the premium amount of diabetic patients in presence of predictors or covariates. The risk factors responsible for the cause of the diabetic patients have also been identified using Logistic GAM. The procedure has been applied to a real life data set of 134 diabetic patients by smoothening the effect of covariates.

15

Authors: Juan F. Navarro

The Poincaré–Lindstedt method in perturbation theory is used to compute periodic solutions in perturbed differential equations through a nearby periodic orbit of the unperturbed problem. The adaptation of this technique to systems of differential equations of first order could produce meaningful advances in the qualitative analysis of many dynamical systems. In this paper, we present a new symbolic algorithm as well as a new symbolic computation tool to calculate periodic solutions in systems of differential equations of first order. The algorithm is based on an optimized adaptation of the Poincaré–Lindstedt technique to differential systems. This algorithm is applied to compute a periodic solution in a Lotka–Volterra system.

7

Authors: Hetal Shah, Jigisha Pandya, Pinky Shah

This paper aims to present the approximate solution for a thin film flow of a third grade fluid down an inclined plane. The variation of the velocity field for different parameters has been analyzed. The spline collocation method is used to obtain the accurate solution. The results are shown in a tabular form as well as in a graphical manner.

8

Authors: Nita H. Shah, Bijal M. Yeolekar

The dynamics of a fishery resource system is formulated for fish harvesting with effort and price-sensitive demand. The model considers deterioration as damage during catchability. It is assumed that the supply is instantaneous. The system of non-linear differential equations is formulated and solved to determine the non-trivial equilibrium. The conditions for stability of equilibria are worked out. The numerical data are used to support theoretical results derived.

13

Authors: Mykhail Moskalkov, Dauletbay Utebaev

In this paper, on the basis of a numerical finite element method, the solution of the Neumann problem with respect to the oscillation equation for gravity-gyroscopic waves is discussed. The approximation with respect to spatial variables is achieved by using linear splines, and the approximation with respect to time is achieved by using cubic Hermitean splines. It is demonstrated that the use of such approximation with respect to time allows the quality of the solution to be essentially improved as compared with the traditional approximation ensuring the second order accuracy. The stability and accuracy of the method are estimated. Using the method of regularization with spectrum shift, a new method is developed for solving the spatial operator degeneration problem associated with the Neumann problem. The results of the numerical calculations performed provide the possibility to make conclusions on the mode of behavior of the solution of the Neumann problem depending on the problem variables.

10

Authors: Alexander G. Ramm , Mykhaylo I. Andriychuk

A nonlinear antenna synthesis problem is considered. Given a function that approximates the modulus of the diagram, an explicit formula for the corresponding current is found. This current generates the diagram as close to the given function as one wants. The numerical results illustrating the developed method are presented. The results show that in order to achieve a desired accuracy of approximation of the given function by the modulus of the diagram one may use currents that oscillates much.

14

Authors: Navnit Jha, Ravindra Kumar, R. K. Mohanty

An approximate solution technique based on non-polynomial spline and finite difference method has been described for two-space dimensional quasi-linear elliptic boundary value problems. The numerical scheme in the limiting case of non-polynomial spline parameter provides the cubic spline scheme. The proposed scheme is analyzed for the convergence using matrix theory. Experimental results show the importance of using non-polynomial spline scheme over corresponding cubic spline scheme in terms of iterations to achieve desired accuracy. The method is tested for the convergence and corroborates the theoretical truncation errors. The accuracy in the solutions is obtained for Tricomi and KhokhlovZabolotskaya equations for various mesh step sizes.

15

Authors: A. Anguraj, S. Kanjanadevi

In this paper, we prove the existence results for fractional integro-differential equations with fractional order non-instantaneous impulsive conditions. We prove the existence of mild solutions by using the resolvent operator and fixed point theorem for condensing map.