Applied Mathematics Commons^™

Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim.

On Numerical Solutions Of Two-Dimensional Boussinesq Equations By Using Adomian Decomposition And He's Homotopy Perturbation Method, Syed T. Mohyud-Din, Mustafa Inc, Ebru Cavlak

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we obtain the approximate solution for 2-dimensional Boussinesq equation with initial condition by Adomian's decomposition and homotopy perturbation methods and numerical results are compared with exact solutions.

Exact Solitary-Wave Special Solutions For The Nonlinear Dispersive K(M,N) Equations By Means Of The Homotopy Analysis Method, Ahmet Yıldırım, Canan Ünlü, Syed T. Mohyud-Din

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the nonlinear dispersive K(m,n) equations which exhibit solutions with solitary patterns. New exact solitary solutions are found. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete features of the homotopy analysis method in K(m,n) equations. The nonlinear equations K(m,n) are studied for two different cases, namely when m = n being odd and even integers. General formulas for the solutions of K(m,n) equations are established.

A Note On He’S Parameter-Expansion Method Of Coupled Van Der Pol–Duffing Oscillators, N. H. Sweilam, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents the analytical and approximate solutions of the coupled chaotic Van der Pol-Duffing systems, by using the He's parameter-expansion method (PEM). One iteration is sufficient to obtain a highly accurate solution, which is valid for the whole solution domain. From the obtained results, we can conclude that the suggest method, is of utter simplicity, and can be easily extended to all kinds of non-linear equations.

Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is applied to some nonlinear second order initial value problems and the numerical results reveal that the modified method is accurate and efficient for second order initial value problems.

Forced Oscillations Of Nonlinear Hyperbolic Equations With Functional Arguments Via Riccati Method, Yutaka Shoukaku

Applications and Applied Mathematics: An International Journal (AAM)

By using integral averaging method and a generalized Riccati technique, sufficient conditions are established for the oscillation of solutions of forced nonlinear hyperbolic equations with functional arguments.

Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel

Applications and Applied Mathematics: An International Journal (AAM)

The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution.

The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the variational iteration method is applied for finding the solution of an Integro-differential parabolic problem with integral conditions. Convergence of the proposed method is also discussed. Finally, some numerical examples are given to show the effectiveness of the proposed method.

Revised Variational Iteration Method For Solving Systems Of Ordinary Differential Equations, Elham Salehpoor, Hossein Jafari, Merieh A. Afrapoli

Applications and Applied Mathematics: An International Journal (AAM)

A modification of the variational iteration method applied to systems of linear/non-linear ordinary differential equations, which yields a series solution with accelerated convergence, has been presented. Illustrative examples have been given.

An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta

Applications and Applied Mathematics: An International Journal (AAM)

In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.

Dnagents: Genetically Engineered Intelligent Mobile Agents, Jeremy Otho Kackley

Dissertations

Mobile agents are a useful paradigm for network coding providing many advantages and disadvantages. Unfortunately, widespread adoption of mobile agents has been hampered by the disadvantages, which could be said to outweigh the advantages. There is a variety of ongoing work to address these issues, and this is discussed. Ultimately, genetic algorithms are selected as the most interesting potential avenue. Genetic algorithms have many potential benefits for mobile agents. The primary benefit is the potential for agents to become even more adaptive to situational changes in the environment and/or emergent security risks. There are secondary benefits such as the natural …

Quantum Codes From Two-Point Hermitian Codes, Justine Hyde-Volpe

All Theses

We explore the background on error-correcting codes, including linear codes and quantum codes from curves. Then we consider the parameters of quantum codes constructed from two-point Hermitian codes.

Contaminant Flow And Transport Simulation In Cracked Porous Media Using Locally Conservative Schemes, Pu Song

All Theses

The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous media, such as the influence of fracture network on the advection and diffusion of contaminant species, the adsorption impact of contaminant wastes on the overall transport flow and so on. In order to precisely describe the whole process, we firstly need to build the mathematical model to simulate this problem numerically. Taking into consideration of the characteristics of contaminant flow, we employ two partial differential equations to formulate the whole problem. One is flow equation, the other is reactive transport equation. The first …

A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt

University Faculty Publications and Creative Works

Let M3 S C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-Hermitian part of the second fundamental form transforms under Möbius transformations. The surfaces for which these forms are constant multiples of each other were identified in previous work, provided the constant is not unimodular. Here it is proved that if the surface is assumed to be complete and if the constant is unimodular, then the surface is tubed over a strongly convex curve. The converse statement is true, too, and is easily …

A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt

University Faculty Publications and Creative Works

Let M3 S C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-Hermitian part of the second fundamental form transforms under Möbius transformations. The surfaces for which these forms are constant multiples of each other were identified in previous work, provided the constant is not unimodular. Here it is proved that if the surface is assumed to be complete and if the constant is unimodular, then the surface is tubed over a strongly convex curve. The converse statement is true, too, and is easily …

Elements Of Study On Dynamic Materials, Marine Rousseau, Gerard A. Maugin, Mihhail Berezovski

Publications

As a preliminary study to more complex situations of interest in small-scale technology, this paper envisages the elementary propagation properties of elastic waves in one-spatial dimension when some of the properties (mass density, elasticity) may vary suddenly in space or in time, the second case being of course more original. Combination of the two may be of even greater interest. Toward this goal, a critical examination of what happens to solutions at the crossing of pure space-like and time-like material discontinuities is given together with simple solutions for smooth transitions and numerical simulations in the discontinuous case. The effects on …

Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He

Scholarship

A boundary type quadrature formula (BTQF) is an approximate integration formula with all its of evaluation points lying on the Boundary of the integration domain. This type formulas are particularly useful for the cases when the values of the integrand functions and their derivatives inside the domain are not given or are not easily determined. In this paper, we will establish the BTQFs over sonic axially symmetric regions. We will discuss time following three questions in the construction of BTQFs: (i) What is the highest possible degree of algebraic precision of the BTQF if it exists? (ii) What is the …

The Generation Of Domestic Electricity Load Profiles Through Markov Chain Modelling, Aidan Duffy, Fintan Mcloughlin, Michael Conlon

Conference Papers

Micro-generation technologies such as photovoltaics and micro-wind power are becoming increasing popular among homeowners, mainly a result of policy support mechanisms helping to improve cost competiveness as compared to traditional fossil fuel generation. National government strategies to reduce electricity demand generated from fossil fuels and to meet European Union 20/20 targets is driving this change. However, the real performance of these technologies in a domestic setting is not often known as high time resolution models for domestic electricity load profiles are not readily available. As a result, projections in terms of reducing electricity demand and financial paybacks for these micro-generation …

Post-Processing Techniques And Wavelet Applications For Hammerstein Integral Equations, Khomsan Neamprem

Mathematics & Statistics Theses & Dissertations

This dissertation is focused on the varieties of numerical solutions of nonlinear Hammerstein integral equations. In the first part of this dissertation, several acceleration techniques for post-processed solutions of the Hammerstein equation are discussed. The post-processing techniques are implemented based on interpolation and extrapolation. In this connection, we generalize the results in [29] and [28] to nonlinear integral equations of the Hammerstein type. Post-processed collocation solutions are shown to exhibit better accuracy. Moreover, an extrapolation technique for the Galerkin solution of Hammerstein equation is also obtained. This result appears new even in the setting of the linear Fredholm equation.

In …

A Solution Of The Heat Equation With The Discontinuous Galerkin Method Using A Multilivel Calculation Method That Utilizes A Multiresolution Wavelet Basis, Robert Gregory Brown

Mathematics & Statistics Theses & Dissertations

A numerical method to solve the parabolic problem is developed that utilizes the Discontinuous Galerkin Method for space and time discretization. A multilevel method is employed in the space variable. It is shown that use of this process yields the same level of accuracy as the standard Discontinuous Galerkin Method for the heat equation, but with cheaper computational cost. The results are demonstrated using a standard one-dimensional homogeneous heat problem.

Symmetries Of The Central Vestibular System: Forming Movements For Gravity And A Three-Dimensional World, Gin Mccollum, Douglas Hanes

Mathematics and Statistics Faculty Publications and Presentations

Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified by geometric conditions. Symmetry groups have been found to structure experimentally-recorded pathways of the central vestibular system. When related to geometric conditions in three-dimensional physical space, these symmetry groups make sense as a logical foundation for sensorimotor coordination.

Analytic Construction Of Periodic Orbits In The Restricted Three-Body Problem, Mohammed A. Ghazy

Mechanical & Aerospace Engineering Theses & Dissertations

This dissertation explores the analytical solution properties surrounding a nominal periodic orbit in two different planes, the plane of motion of the two primaries and a plane perpendicular to the line joining the two primaries, in the circular restricted three-body problem. Assuming motion can be maintained in the plane and motion of the third body is circular, Jacobi's integral equation can be analytically integrated, yielding a closed-form expression for the period and path expressed with elliptic integral and elliptic function theory. In this case, the third body traverses a circular path with nonuniform speed. In a strict sense, the in-plane …

Extended Second Welfare Theorem For Nonconvex Economies With Infinite Commodities And Public Goods, Aychiluhim Habte, Boris S. Mordukhovich

Mathematics Research Reports

This paper is devoted to the study of nonconvex models of welfare economics with public goods and infinite-dimensional commodity spaces. Our main attention is paid to new extensions of the fundamental second welfare theorem to the models under consideration. Based on advanced tools of variational analysis and generalized differentiation, we establish appropriate approximate and exact versions of the extended second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations in both marginal price and decentralized price forms.

Optimizing Radiology Peer Review: A Mathematical Model For Selecting Future Cases Based On Prior Errors, Yun Robert Sheu, Elie Feder, Igor Balsim, Victor F. Levin, Andrew G. Bleicher, Barton F. Branstetter Iv

Publications and Research

Introduction: Peer review is an essential process for physicians because it facilitates improved quality of patient care and continuing physician learning and improvement. However, peer review often is not well received by radiologists, who note that it is time intensive, subjective, and lacks demonstrable impact on patient care. Current advances in peer review include the RADPEER system with its standardization of discrepancies and incorporation of the peer review process into the PACS itself. Our purpose was to build on RADPEER and similar systems by using a mathematical model to optimally select the types of cases to be reviewed, for each …

Solutions Of Tenth And Ninth-Order Boundary Value Problems By Modified Variational Iteration Method, Syed Tauseef Mohyud-Din, Ahmet Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the modified variational iteration method (MVIM) for solving the ninth and tenth-order boundary value problems. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm …

A Resource Based Stage-Structured Fishery Model With Selective Harvesting Of Mature Species, T. K. Kar, Swarnakamal Misra

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have considered a model in which revenue is generated from fishing and the growth of the fish depends upon the plankton which in turn follows a logistic law of growth. Here the fish population has two stages, a juvenile stage and a mature stage and we consider the harvesting of the mature fish species. Stability and permanence of the system are discussed. Maximum sustainable yield, maximum economic yield and optimal sustainable yield are obtained and different tax policies are discussed to achieve the reference points.

Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.

Bianchi Type I Bulk Viscous Fluid String Dust Cosmological Model With Magnetic Field In Bimetric Theory Of Gravitation, M. S. Borkar, S. S. Charjan

Applications and Applied Mathematics: An International Journal (AAM)

In the presence of both magnetic field and bulk viscosity, Bianchi Type I bulk viscous fluid string dust cosmological model in Rosen’s bimetric theory of gravitation have been investigated by using the technique of Letelier and Stachel. The nature of the model is discussed in the absence of both magnetic field and bulk viscosity. To get a determinate solution, we have assumed the condition that σ is proportional to θ and ζθ = constant where σ is the shear, θ is the expansion in the model and ζ is the coefficient of bulk viscosity. Further the physical and geometrical significance …

Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.

Comparison Differential Transformation Technique With Adomian Decomposition Method For Dispersive Long-Wave Equations In (2+1)-Dimensions, M. A. Mohamed

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we will introduce two methods to obtain the numerical solutions for the system of dispersive long-wave equations (DLWE) in (2+1)-dimensions. The first method is the differential transformation method (DTM) and the second method is Adomian decomposition method (ADM). Moreover, we will make comparison between the solutions obtained by the two methods. Consequently, the results of our system tell us the two methods can be alternative ways for solution of the linear and nonlinear higher-order initial value problems.