Applied Mathematics Commons^™

On The Stability Of First Order Ordinary Differential Equation With A Nonlocal Condition, Ebtisam Omer Bin-Taher

Hadhramout University Journal of Natural & Applied Sciences

In this paper we study the existence and uniqueness of solution for the first order differential equation,𝑑𝑥𝑑𝑡 + 𝑓(𝑡,𝑥(𝑡))=0,𝑡∈[0,𝑇] with the nonlocal condition 𝑥(1)+ 𝐼𝛾 𝑥(𝑡)|𝑡=𝑡𝑜=𝑥𝑜 ., then we prove that the solution is uniformly stable

Seventh And Twelfth-Order Iterative Methods For Roots Of Nonlinear Equations, Hassan Mohamed Bawazir

Hadhramout University Journal of Natural & Applied Sciences

This study presents two iterative methods, based on Newton’s method, to attain the numerical solutions of nonlinear equations. We prove that our methods have seven and twelve orders of convergence. The analytical investigation has been established to show that our schemes have higher efficiency indexes than some recent methods. Numerical examples are executed to investigate the performance of the proposed schemes. Moreover, the theoretical order of convergence is verified on the numerical examples.

Convergence Properties Of Solutions Of A Length-Structured Density-Dependent Model For Fish, Geigh Zollicoffer

Rose-Hulman Undergraduate Mathematics Journal

We numerically study solutions to a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We make conjectures about the convergence properties of solutions to this equation, and give numerical simulations which support these conjectures. We also study the distribution of biomass in the different age classes as a function of the total biomass.

On The Study Of Age-Related Physiological Decline In C. Elegans, Drew Benjamin Sinha

McKelvey School of Engineering Graduate Student Theses & Dissertations

Aging decline is a universal and unescapable phenomenon; as organisms reach maturity and continue living, physiological function inevitably declines, resulting in mortality. While the study of mortality has been long studied, technical and practical challenges have limited the equally important study of how/when individuals deteriorate and what types of factors affect that deterioration. This gap in knowledge is not only evident in a relative lack of empirical data on physiological decline, but considerable debate around the analysis and conceptual interpretations of the little data that is available.

In this dissertation, I use quantitative reasoning and analysis of longitudinal data to …

Regularity Criteria For The Kuramoto-Sivashinsky Equation In Dimensions Two And Three, Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki

Department of Mathematics: Faculty Publications

We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability criteria for the regularity of solutions in terms of the scalar solution ∅, the vector solution u ≜ ∇∅, as well as the divergence div(u) = Δ∅, and each component of u and ∇u. We also investigate these criteria computationally in the 2D case, and we include snapshots of solutions for several quantities of interest that arise in energy estimates.

Staying One Step Ahead Of The Growing Electric Vehicle Market, Russell Molter

Honors Projects

Electric vehicles are becoming more popular among drivers as they become more affordable and as people become more aware of the benefits of electric vehicles. Because of this, the demand for electric car chargers is quickly increasing across the country. This includes BGSU’s campus. Right now, there are seven chargers available on campus, but with the trends in how the electric vehicle market is growing, BGSU should create a plan to install many more chargers to meet the increasing demand for charging stations. This strategy will allow BGSU to keep up with the growing electric vehicle market, which will additionally …

Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt

Departmental Honors & Graduate Capstone Projects

In this research project, we used numerical methods to investigate trends in the susceptible, exposed, infectious, quarantined, recovered, closed cases and insusceptible populations for the COVID-19 pandemic in 2021. We used the SEIQR model containing seven ordinary differential equations, based on the SIR model for epidemics. An analytical solution was derived from a simplified version of the model, created by making various assumptions about the original model. Numerical solutions were generated for the first 100 days of 2021 using algorithms based on Euler's Method, Runge-Kutta Method, and Multistep Methods. Our goal is to show that numerical methods can help us …

Error Propagation And Algorithmic Design Of Contour Integral Eigensolvers With Applications To Fiber Optics, Benjamin Quanah Parker

Dissertations and Theses

In this work, the finite element method and the FEAST eigensolver are used to explore applications in fiber optics. The present interest is in computing eigenfunctions u and propagation constants β satisfing [sic] the Helmholtz equation Δu + k²n²u = β²u. Here, k is the freespace wavenumber and n is a spatially varying coefficient function representing the refractive index of the underlying medium. Such a problem arises when attempting to compute confinement losses in optical fibers that guide laser light. In practice, this requires the computation of functions u referred to as …

Q-Analogue Modified Laguerre And Generalized Laguerre Polynomials Of Two Variables, Fadhle Bin Fadhle Mohsen, Fadhl Saleh .Alsarahi

Hadhramout University Journal of Natural & Applied Sciences

The 𝑞-Laguerre polynomials are important 𝑞-orthogonal polynomials whose applications and generalizations arise in many applications such as quantumgroup (oscillator algebra, etc.), 𝑞-harmonic oscillator and coding theory. In this paper, we introduce the q-analogue modified Laguerre and generalized modified Laguerre polynomials of two variables . Some recurrence relations for these polynomials are derived.

A Chebyshev Spectral Collocation Method For Solving Kdv-Burgers Equation, Mubarak Awadh Assabaai

Hadhramout University Journal of Natural & Applied Sciences

A mixed spectral/ Runge-Kutta method is used to obtain numerical solutions of Kortewege–de Vries–Burgers’ (KdVB) equation. The suggested method based on Chebyshev spectral collocation is used with Runge-Kutta method of order four. This technique is accomplished by starting with a Chebyshev approximation for the higher order derivatives in the x -direction and generating approximations to the lower derivatives through successive integrations of the highest-order derivative. The proposed technique reduces the problem to a system of ordinary differential equations in the t -direction. The Runge-Kutta method of order four is used to solve this system. Excellent numerical results have been obtained …

Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.

Final Project Report Nsf Award 1744490: Nsf Includes Ddlp: Leadership And Isteam For Females In Elementary School (Life): An Integrated Approach To Increase The Number Of Women Pursuing Careers In Stem, Bruce G. Bukiet, James Lipuma, Nancy Steffen-Fluhr

STEM for Success Resources

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

The LiFE project created and studied a comprehensive program bringing together iSTEAM, holistic student growth, modern technologies, and other supports to engage girls in STEM experiences through a collective impact approach.

LiFE supported STEAM clubs with role models and utilized research-based best …

An Analysis Of Comparison-Based Sorting Algorithms, Jacob M. Gomez, Edgar Aponte, Brad Isaacson

Publications and Research

Our names are Edgar Aponte and Jacob Gomez and we are Applied Mathematics students at City Tech. Our mentor is Prof. Isaacson and we conducted an analysis of comparison-based sorting algorithms, meaning that they can sort items of any type for which a “less-than” relation is defined. We implemented 24 comparison-based sorting algorithms and elaborated on 6 for our poster. We analyzed the running times of these sorting algorithms with various sets of unsorted data and found that introspective sort and timsort were the fastest and most efficient, with introspective sort being the very fastest.

(R1491) Numerical Solution Of The Time-Space Fractional Diffusion Equation With Caputo Derivative In Time By A-Polynomial Method, Saeid Abbasbandy, Jalal Hajishafieiha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a novel type of polynomial is defined which is equipped with an auxiliary parameter a. These polynomials are a combination of the Chebyshev polynomials of the second kind. The approximate solution of each equation is assumed as the sum of these polynomials and then, with the help of the collocation points, the unknown coefficients of each polynomial, as well as auxiliary parameter, is obtained optimally. Now, by placing the optimal value of a in polynomials, the polynomials are obtained without auxiliary parameter, which is the restarted step of the present method. The time discretization is performed …

(R1480) Heat Transfer In Peristaltic Motion Of Rabinowitsch Fluid In A Channel With Permeable Wall, Mahadev M. Channakote, Dilipkumar V. Kalse

Applications and Applied Mathematics: An International Journal (AAM)

This paper is intended to investigate the effect of heat transfer on the peristaltic flow of Rabinowitsch fluid in a channel lined with a porous material. The Navier -Stokes equation governs the channel's flow, and Darcy's law describes the permeable boundary. The Rabinowitsch fluid model's governing equations are solved by utilizing approximations of the long-wavelength and small number of Reynolds. The expressions for axial velocity, temperature distribution, pressure gradient, friction force, stream function are obtained. The influence on velocity, pressure gradient, friction force, and temperature on pumping action of different physical parameters is explored via graphs.

(R1497) On The Invariant Subspaces Of The Fractional Integral Operator, Mehmet Gürdal, Anar Adiloglu Nabiev, Meral Ayyıldız

Applications and Applied Mathematics: An International Journal (AAM)

In operator theory, there is an important problem called the invariant subspace problem. This important problem of mathematics has been clear for more than half a century. However the solution seems to be nowhere in sight. With this motivation, we investigate the invariant subspaces of the fractional integral operator in the Banach space with certain conditions in this paper. Also by using the Duhamel product method, unicellularity of the fractional integral operator on some space is obtained and the description of the invariant subspaces is given.

(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez

Applications and Applied Mathematics: An International Journal (AAM)

In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number …

(R1056) Effect Of Rotation On Plane Waves Of Generalized Magneto-Thermoelastic Medium With Voids Under Thermal Loading Due To Laser Pulse, Mohamed I.A. Othman, Ezaira R.M. Edeeb

Applications and Applied Mathematics: An International Journal (AAM)

The investigation in this paper deals with the rotation of the magneto-thermoelastic solid and with voids subjected to thermal loading due to laser pulse. The problem is studied in the context of three theories of generalized magneto thermoelasticity: Lord-Schulman (L-S), Green-Lindsay (G-L) and the coupled theory (CD) with the effect of rotation, magnetic field, thermal loading and voids. The methodology applied here is using the normal mode analysis to solve the physical problem to obtain the exact expressions for the displacement components, the stresses, the temperature, and the change in the volume fraction field have been shown graphically by comparison …

(R1513) The Dynamical Study Of Variable Mass Test Particle In Nonlinear Sense Of Restricted 3-Body Problem With Heterogeneous Primaries, Sada Nand Prasad, Kumari Shalini, Abdullah A. Ansari

Applications and Applied Mathematics: An International Journal (AAM)

The main idea of this paper is to study the non-linear stability property of the motion of the test particle which is moving under the influence of heterogeneous primaries having N-layers with different densities as well as varying its mass according to Jeans law. The system is also perturbed by the small perturbations in Coriolis as well as centrifugal forces. We evaluate the equations of motion of the test particle under the influence of the above said perturbations. From this system of equations of motion, we reveal analytically the locations of stationary points as well as the non-linear stability.

(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat

Applications and Applied Mathematics: An International Journal (AAM)

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …