# Numerical Analysis and Computation Commons™

## All Articles in Numerical Analysis and Computation

1,035 full-text articles. Page 7 of 38.

One-Note-Samba Approach To Cosmology, 2019 University of New Mexico

#### One-Note-Samba Approach To Cosmology, Florentin Smarandache, Victor Christianto

##### Mathematics and Statistics Faculty and Staff Publications

Inspired by One Note Samba, a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology. Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also briefly discuss possible link with our previous paper which describes Newtonian Universe with Vortex in terms of Ermakov equation.

2019 Boise State University

#### Radial Basis Function Finite Difference Approximations Of The Laplace-Beltrami Operator, Sage Byron Shaw

##### Boise State University Theses and Dissertations

Partial differential equations (PDEs) are used throughout science and engineering for modeling various phenomena. Solutions to PDEs cannot generally be represented analytically, and therefore must be approximated using numerical techniques; this is especially true for geometrically complex domains. Radial basis function generated finite differences (RBF-FD) is a recently developed mesh-free method for numerically solving PDEs that is robust, accurate, computationally efficient, and geometrically flexible. In the past seven years, RBF-FD methods have been developed for solving PDEs on surfaces, which have applications in biology, chemistry, geophysics, and computer graphics. These methods are advantageous, as they are mesh-free, operate on arbitrary ...

Exploring Delay Dispersal In Us Airport Network, 2019 California State University, Northridge

#### Exploring Delay Dispersal In Us Airport Network, Brandon Sripimonwan, Arun Sathanur

##### STAR Program Research Presentations

The modeling of delay diffusion in airport networks can potentially help develop strategies to prevent the spread of such delays and disruptions. With this goal, we used the publicly-available historical United States Federal Aviation Administration (FAA) flight data to model the spread of delays in the US airport network. For the major (ASPM-77) airports for January 2017, using a threshold on the volume of flights, we sparsify the network in order to better recognize patterns and cluster structure of the network. We developed a diffusion simulator and greedy optimizer to find the top influential airport nodes that propagate the most ...

2019 University of Southern Mississippi

#### Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley

##### Master's Theses

For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in one-dimension with two cases to observe the behaviors of the errors using KSS methods. The first case will implement KSS methods with trigonometric initial conditions, then another case where the initial conditions are polynomial functions. We will also look at both the time-independent and time-dependent ...

Trefftz Finite Elements On Curvilinear Polygons, 2019 Indian Institute of Technology Kanpur

#### Trefftz Finite Elements On Curvilinear Polygons, Akash Anand, Jeffrey S. Ovall, Samuel E. Reynolds, Steffen Weisser

##### Mathematics and Statistics Faculty Publications and Presentations

We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in the formation of local stiffness matrices. To define our local finite element spaces in the presence of curved edges, we must also properly define what it means for a function defined on a curved edge to be "polynomial" of a given degree on that edge. We consider two natural choices, before settling on the one that yields the inclusion of complete polynomial spaces in our local ...

2019 The University of Western Ontario

#### Some Recent Developments On Pareto-Optimal Reinsurance, Wenjun Jiang

##### Electronic Thesis and Dissertation Repository

This thesis focuses on developing Pareto-optimal reinsurance policy which considers the interests of both the insurer and the reinsurer. The optimal insurance/reinsurance design has been extensively studied in actuarial science literature, while in early years most studies were concentrated on optimizing the insurer’s interests. However, as early as 1960s, Borch argued that “an agreement which is quite attractive to one party may not be acceptable to its counterparty” and he pioneered the study on “fair” risk sharing between the insurer and the reinsurer. Quite recently, the question of how to strike a balance in risk sharing between an ...

2019 University of South Florida

#### Graphicacy For Numeracy: Review Of Fundamentals Of Data Visualization: A Primer On Making Informative And Compelling Figures By Claus O. Wilke (2019), Christy M. Bebeau

##### Numeracy

Wilke, Claus O. 2019. Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures. (Sebastopol, CA: O’Reilly Media, Inc.). 390 pp. ISBN 978-1-492-03108-6. First edition. First release: 03-15-2019.

Claus O. Wilke has authored an excellent reference about producing and understanding static figures, figures used online, in print, and for presentations. His book is neither a statistics nor programming text, but familiarity with basic statistical concepts is helpful. Written in three parts, the book presents both the math and artistic design aspects of telling a story through figures. Wilke makes extensive use of examples, labels them good, bad ...

2019 University of Massachusetts Amherst

#### Asymptotic And Numerical Analysis Of Coherent Structures In Nonlinear Schrodinger-Type Equations, Cory Ward

##### Doctoral Dissertations

This dissertation concerns itself with coherent structures found in nonlinear Schrödinger-type equations and can be roughly split into three parts. In the first part we study a deformation of the defocusing nonlinear Schrödinger (NLS) equation, the defocusing Camassa-Holm NLS (CH-NLS) equation in both one and two space dimensions. We use asymptotic multiscale expansion methods to reduce this model to a Boussinesq-like equation, which is then subsequently used to obtain approximate solitary wave solutions for both the 1D and 2D CH-NLS equations. We then use direct numerical simulations to investigate the validity of these approximate solutions, their evolution, and their head-on ...

Runge–Kutta–Gegenbauer Explicit Methods For Advection-Diffusion Problems, 2019 Technological University Dublin

#### Runge–Kutta–Gegenbauer Explicit Methods For Advection-Diffusion Problems, Stephen O'Sullivan

##### Articles

In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial degree, and in the imaginary direction as an increasing function of Gegenbauer parameter. Consequently, the polynomials are naturally suited to the construction of high order stabilized Runge-Kutta (SRK) explicit methods for systems of PDEs of mixed hyperbolic-parabolic type.

We present SRK methods composed of L ordered forward Euler stages, with complex-valued stepsizes derived from the roots of RKG stability polynomials of degree $L$. Internal stability ...

The Isometry Degree Of A Computable Copy Of ℓp, 2019 Iowa State University

#### The Isometry Degree Of A Computable Copy Of ℓp, Timothy H. Mcnicholl, Donald M. Stull

##### Mathematics Publications

When p is a computable real so that p⩾1, we define the isometry degree of a computable presentation of ℓp to be the least powerful Turing degree d by which it is d-computably isometrically isomorphic to the standard presentation of ℓp. We show that this degree always exists and that when p≠2 these degrees are precisely the c.e. degrees.

Boundary Value Problem For Nonhomogeneous Mixed-Type Equation With Two Degenerate Lines, 2019 Turin Polytechnic University, Kichik Halka yuli 17, Tashkent 100095, Uzbekistan.

#### Boundary Value Problem For Nonhomogeneous Mixed-Type Equation With Two Degenerate Lines, K.S. Fayazov, Y. K. Khudayberganov

##### Acta of Turin Polytechnic University in Tashkent

In this work, we study boundary value problem for nonhomogeneous mixed-type equation with two degenerate lines. A priori estimate for the solution of the problem is obtained, theorems of uniqueness and conditional stability in the set of correctness are proved. The approximate solution by the regularization method has been constructed.

An Epidemiological Model With Simultaneous Recoveries, 2019 University of Maine

#### An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber

##### Electronic Theses and Dissertations

Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way of a ...

School Policy Evaluated With Time-Reversible Markov Chain, 2019 University of Connecticut - Storrs

#### School Policy Evaluated With Time-Reversible Markov Chain, Trajan Murphy, Iddo Ben-Ari

##### Honors Scholar Theses

In this work we propose a reversible Markov chain scheme to model for the mobility of students affected by a grade school leveling policy. This model provides unified and mathematically tractable framework in which transition functions are sampled uniformly from the set of {\bf reversible} transition functions. The results from the study appear to confirm the disadvantageous effects of this school policy, on par with the of a previous model on the same policy.

Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, 2019 Marshall University

#### Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, Olusegun M. Otunuga, Anna Mummert

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, 2019 Cooper Union for the Advancement of Science and Art

#### Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Immunofluorescence Image Feature Analysis And Clustering Pipeline For Distinguishing Epithelial-Mesenchymal Transition, 2019 Virginia Commonwealth University

#### Immunofluorescence Image Feature Analysis And Clustering Pipeline For Distinguishing Epithelial-Mesenchymal Transition, Shreyas Hirway, Nadiah Hassan, Dr. Christopher Lemmon, Dr. Seth Weinberg

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

2019 State University of New York at New Paltz

#### Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu

##### Biology and Medicine Through Mathematics Conference

No abstract provided.

Paper Structure Formation Simulation, 2019 University of Maine

#### Paper Structure Formation Simulation, Tyler R. Seekins

##### Electronic Theses and Dissertations

On the surface, paper appears simple, but closer inspection yields a rich collection of chaotic dynamics and random variables. Predictive simulation of paper product properties is desirable for screening candidate experiments and optimizing recipes but existing models are inadequate for practical use. We present a novel structure simulation and generation system designed to narrow the gap between mathematical model and practical prediction. Realistic inputs to the system are preserved as randomly distributed variables. Rapid fiber placement (~1 second/fiber) is achieved with probabilistic approximation of chaotic fluid dynamics and minimization of potential energy to determine flexible fiber conformations. Resulting digital ...

#### The Effects Of Finite Precision On The Simulation Of The Double Pendulum, Rebecca Wild

##### Senior Honors Projects, 2010-2019

We use mathematics to study physical problems because abstracting the information allows us to better analyze what could happen given any range and combination of parameters. The problem is that for complicated systems mathematical analysis becomes extremely cumbersome. The only effective and reasonable way to study the behavior of such systems is to simulate the event on a computer. However, the fact that the set of floating-point numbers is finite and the fact that they are unevenly distributed over the real number line raises a number of concerns when trying to simulate systems with chaotic behavior. In this research we ...

2019 University of Southern Mississippi

#### Enhancement Of Krylov Subspace Spectral Methods Through The Use Of The Residual, Haley Dozier

##### Dissertations

Depending on the type of equation, finding the solution of a time-dependent partial differential equation can be quite challenging. Although modern time-stepping methods for solving these equations have become more accurate for a small number of grid points, in a lot of cases the scalability of those methods leaves much to be desired. That is, unless the timestep is chosen to be sufficiently small, the computed solutions might exhibit unreasonable behavior with large input sizes. Therefore, to improve accuracy as the number of grid points increases, the time-steps must be chosen to be even smaller to reach a reasonable solution ...