Applied Mathematics Commons^™

Kink, Singular Soliton And Periodic Solutions To Class Of Nonlinear Equations, Marwan Alquran, Safwan Al-Shara, Sabreen Al-Nimrat

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we extend the ordinary differential Duffing equation into a partial differential equation. We study the traveling wave solutions to this model by using the G'/G expansion method. Then, based on the obtained results given for the Duffing equation, we generate kink, singular soliton and periodic solutions for a coupled integrable dispersionless nonlinear system. All the solutions given in this work are verified.

Generating Random Vectors Using Transformation With Multiple Roots And Its Applications, Qidi Peng, Henry Schellhorn, Lu Zhu

Applications and Applied Mathematics: An International Journal (AAM)

An approach is proposed to generate random vectors using transformation with multiple roots. This approach generalizes the one-dimensional inverse transformation with multiple roots method to higher dimensions, i.e., to random vectors with or without densities. In this approach, multiple roots of the transformation and probabilities of selecting each of the roots are derived. The strategies for constructing such a transformation are discussed and several examples are presented to motivate this simulation approach.

A Note On An M/M/S Queueing System With Two Reconnect And Two Redial Orbits, Amina A. Bouchentouf, Hanane Sakhi

Applications and Applied Mathematics: An International Journal (AAM)

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new …

New Exact Solutions Of The Perturbed Nonlinear Fractional Schr¨Odinger Equation Using Two Reliable Methods, Nasir Taghizadeh, Mona N. Foumani, Vahid S. Mohammadi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the fractional derivatives in the sense of the modified Riemann-Liouville derivative and the first integral method and the Bernoulli sub-ODE method are employed for constructing the exact complex solutions of the perturbed nonlinear fractional Schr ¨odinger equation and comparing the solutions.

Analysis Of Repairable M[X]/(G1,G2)/1 - Feedback Retrial G-Queue With Balking And Starting Failures Under At Most J Vacations, P. Rajadurai, M. C. Saravanarajan, V. M. Chandrasekaran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of services and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them get into the orbit. The negative customer, is arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters the orbit or leaves the system. If the orbit is empty at the service completion of each type …

Optimal Solution Of A Fully Fuzzy Linear Fractional Programming Problem By Using Graded Mean Integration Representation Method, Moumita Deb, P. K. De

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, the study of fully fuzzy linear fractional programming problem (FFLFPP) using graded mean integration representation method is discussed where all the parameters and variables are characterized by trapezoidal fuzzy numbers. A computational algorithm has been presented to obtain an optimal solution by applying simplex method. To demonstrate the applicability of the proposed approach, one numerical example is solved. Also to check the efficiency and feasibility of the proposed approach, we compare the results of examples by applying crisp numbers, triangular fuzzy numbers and trapezoidal fuzzy numbers.

Hyers-Ulam And Hyers-Ulam-Aoki-Rassias Stability For Linear Ordinary Differential Equations, A. N. Mohapatra

Applications and Applied Mathematics: An International Journal (AAM)

Here we prove the Hyers-Ulam stability and Hyers-Ulam-Aoki-Rassias stability of the n-th order ordinary linear differential equation with smooth coefficients on compact and semi-bounded intervals using successive integration by parts. Keywords:

Mathematical Modeling And Analysis Of Leukemia: Effect Of External Engineered T Cells Infusion, Manju Agarwal, Archana S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a nonlinear model is proposed and analyzed to study the spread of Leukemia by considering the effect of genetically engineered patients T cells to attack cancer cells. The model is governed by four dependent variables namely; naive or susceptible blood cells, infected or dysfunctional blood cells, cancer cells and immune cells. The model is analyzed by using the stability theory of differential equations and numerical simulation. We have observed that the system is stable in the local and global sense if antigenicity rate or rate of stimulation of immune cells is greater than a threshold value dependent …

Solution Of Fractional Drinfeld-Sokolov-Wilson Equation Using Homotopy Perturbation Transform Method, P. K. Singh, K. Vishal, T. Som

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the approximate solutions of the non-linear Drinfeld-Sokolov-Wilson equation with fractional time derivative have been obtained. The fractional derivative is described in the Caputo sense. He’s polynomial is used to tackle the nonlinearity which arise in our considered problems. A time fractional nonlinear partial differential equation has been computed numerically. The numerical procedures illustrate the effectiveness and reliability of the method. Effects of fractional order time derivatives on the solutions for different particular cases are presented through graphs.

Optimal Error Estimate Of Upwind Scheme On Adaptive Grid For Two Parameter Singular Perturbation Problem, J. Mohapatra, M. K. Mahalik

Applications and Applied Mathematics: An International Journal (AAM)

A singularly perturbed convection-diffusion problem with two small parameters is considered. The problem is solved by an upwind finite difference operator on an appropriate non-uniform mesh constructed adaptively by equi-distributing a monitor function based on the solution. An error bound in the maximum norm is established theoretically with the error constants shown to be independent of both singular perturbation parameters. The normalized flux obtained via interpolating the polynomial from the numerical solution is also uniformly convergent. A numerical experiment illustrates in practice the result of convergence proved theoretically.

Application Of Reduced Differential Transform Method For Solving Nonlinear Reaction-Diffusion-Convection Problems, A. Taghavi, A. Babaei, A.` Mohammadpour

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, Reduced differential transform method is presented for solving nonlinear reactiondiffusion- convection initial value problems. The methodology with some known techniques shows that the present approach is simple and effective.To show the efficiency of the present method, four interesting examples is given.

A Hybrid Variational Iteration Method For Blasius Equation, M. Sajid, N. Ali, T. Javed

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to present the hybrid variational iteration method. The proposed algorithm is based on the combination of variational iteration and shooting methods. In the proposed algorithm the entire domain is divided into subintervals to establish the accuracy and convergence of the approximate solution. It is found that in each subinterval a three term approximate solution using variational iteration method is sufficient. The proposed hybrid variational iteration method offers not only numerical values, but also closed form analytic solutions in each subinterval. The method is implemented using an example of the Blasius equation. The results show …

On Some Optimal Multiple Root-Finding Methods And Their Dynamics, Munish Kansal, V. Kanwar, Saurabh Bhatia

Applications and Applied Mathematics: An International Journal (AAM)

Finding multiple zeros of nonlinear functions pose many difficulties for many of the iterative methods. In this paper, we present an improved optimal class of higher-order methods for multiple roots having quartic convergence. The present approach of deriving an optimal class is based on weight function approach. In terms of computational cost, all the proposed methods require three functional evaluations per full iteration, so that their efficiency indices are 1.587 and, are optimal in the sense of Kung-Traub conjecture. It is found by way of illustrations that they are useful in high precision computing enviroments. Moreover, basins of attraction of …

Thermal Stresses In Functionally Graded Hollow Sphere Due To Non-Uniform Internal Heat Generation, S. P. Pawar, K. C. Deshmukh, G. D. Kedar

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the thermal stresses in a hollow thick sphere of functionally graded material subjected to non-uniform internal heat generation are obtained as a function of radius to an exact solution by using the theory of elasticity. Material properties and heat generation are assumed as a function of radius of sphere and Poisson’s ratio as constant. The distribution of thermal stresses for different values of the powers of the module of elasticity and varying power law index of heat generation is studied. The results are illustrated numerically and graphically.

A Stage-Structured Two Species Competition Mathematical Model Under The Effect Of Disease, Manju Agarwal, Vinay Verma

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study the dynamics of two competing species model; one of this competing species is stage structured and the disease spreads only in the other competing specie. In order to keep the model simple, we present it under the strong assumption that the disease can not cross the species barrier. Dynamical behaviors such as positivity, boundedness, stability, bifurcation and persistence of the model are studied analytically using the theory of differential equations. Computer simulations are carried out to substantiate the analytical findings. It is noted that c the loss rate of the population, T the maturation time …

Implicit-Explicit Higher-Order Time Integration Schemes For Computations Of Structural Dynamics With Fluid-Structure Interaction, José C. Pedro, Mapundi K. Banda, Precious Sibanda

Applications and Applied Mathematics: An International Journal (AAM)

In this paper higher order implicit Runge-Kutta schemes are applied to fluid-structure interaction (FSI) simulations. A staggered approach with a structural predictor is applied to an FSI problem. The equations governing the dynamics of the structure are integrated in time by the Explicit Single Diagonal Implicit Runge-Kutta (ESDIRK) schemes and the arbitrary high order finite volume scheme is taken as the fluid solver. The performance of the ESDIRK scheme of order of convergence three to five is tested. Comparative studies with other time integration schemes which have been successfully applied to FSI problems are undertaken. Comparisons to test the performance …

Secondary Mathematics Teachers’ Attitudes And Beliefs Toward Statistics: Developing An Initial Profile, Christina M. Zumbrun

Dissertations

Over the last several decades, mathematics education researchers have given increased attention to students’ and teachers’ attitudes and beliefs toward mathematics and statistics, but no work has been done that examines practicing secondary mathematics teachers’ (SMTs’) attitudes and beliefs towards statistics in light of the GAISE framework and the Common Core State Standards for Mathematics (CCSSM). This study begins to address this gap in the research by creating the Teacher Attitude and Beliefs toward Statistics Survey (TABSS), a synthesis of items taken from the Survey of Attitudes Toward Statistics (Schau, 2003), the Statistics Course Attitude Scale and newly developed items …

Edge Colorings Of Graphs And Their Applications, Daniel Johnston

Dissertations

Edge colorings have appeared in a variety of contexts in graph theory. In this work, we study problems occurring in three separate settings of edge colorings.

For more than a quarter century, edge colorings have been studied that induce vertex colorings in some manner. One research topic we investigate concerns edge colorings belonging to this class of problems. By a twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of …

Hydrodynamic Analogues Of Hamiltonian Systems, Francisco J. Jauffred

Graduate Masters Theses

A one-dimensional Hamiltonian system can be modeled and understood as a two-dimensional incompressible fluid in phase space. In this sense, the chaotic behavior of one-dimensional time dependent Hamiltonians corresponds to the mixing of two-dimensional fluids. Amey (2012) studied the characteristic values of one such system and found a scaling law governing them. We explain this scaling law as a diffusion process occurring in an elliptical region with very low eccentricity. We prove that for such a scaling law to occur, it is necessary for a vorticity field to be present. Furthermore, we show that a conformal mapping of an incompressible …

Dynamics Of Locally Coupled Oscillators With Next-Nearest-Neighbor Interaction, J. Herbrych, A. G. Chazirakis, N. Christakis, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

A theoretical description of decentralized dynamics within linearly coupled, one-dimensional oscillators (agents) with up to next-nearest-neighbor interaction is given. Conditions for stability of such system are presented. Our results indicate that the stable systems have response that grow at least linearly in the system size. We give criteria when this is the case. The dynamics of these systems can be described with traveling waves with strong damping in the high frequencies. Depending on the system parameters, two types of solutions have been found: damped oscillations and reflectionless waves. The latter is a novel result and a feature of systems with …