Student Research
Students Research/Stander Symposium Posters (2023)
Ibrahim Guediri
Tim Parson, Adin Stroller, and Henry Stiles
Aaron Hendricks and Jarod Mendoza
Bridget Gerber and Elizabeth Goettke
Students Research/Stander Symposium Posters (2019
1. Computational Mathematics to Study a Model of Complications Due to Diabetes
Poster - Course Project, 201910 MTH 219 05
(Engels Imanol Diaz Gomez, Jeffrey Allen Lott, Nicole Meek)
Abstract:
Diabetes is one of the most popular diseases affecting a large majority of the population. In this project, we use more accurate numerical algorithms to solve the model and compare the results provided in the referenced article. The article uses a basic method known as the Euler’s method to solve the differential equations.
Abstract
Diabetes is one of the most popular diseases affecting a large majority of the population. In this project, we use more accurate numerical algorithms to solve the model and compare the results provided in the referenced article. The article uses a basic method known as the Euler’s method to solve the differential equations.
Students Research/Stander Symposium Posters (2019
1. Computational Mathematics to Study a Model of Complications Due to Diabetes
Poster - Course Project, 201910 MTH 219 05
(Engels Imanol Diaz Gomez, Jeffrey Allen Lott, Nicole Meek)
Abstract:
Diabetes is one of the most popular diseases affecting a large majority of the population. In this project, we use more accurate numerical algorithms to solve the model and compare the results provided in the referenced article. The article uses a basic method known as the Euler’s method to solve the differential equations.
2. The Operator Splitting Method for the Black-Scholes Equation
(Wenfeng Wu, Math Clinic)
Abstract: In the financial industry, the option pricing is an important problem. The Operator Splitting Method is commonly applied to solve initial and boundary value problems of partial differential equations. This project presents the numerical solutions to the Black Scholes Equation using various Operator Splitting Methods. Results are compared with the solutions obtained by a closed-form solution for a European call option.
3. A Comparison of Numerical Solutions of the Black-Scholes Heat Equation for European Call Option
(Lijun Lin, Math Clinic)
Abstract: In this work, we present some numerical solutions to the famous Black-Scholes equation. Although a closed-form solution for the price of European options is available, the prices of more complicated derivatives such as American options may require a numerical solution of the Black-Scholes equation. This poster will focus primarily on the solution to the equation for the European call option.
Students Research/Stander Symposium Posters (2018)
Title: Unique Approaches to the Finite Difference Method (William Shovelton, ME)
Abstract: The oldest and most useful technique to approximate the solution of differential equations is the finite difference method (FDM). This technique allows for derivatives to be replaced by the finite difference discrete approximation, hence we get a finite difference equation (FDE). As with all numerical solutions, this method is only an approximation and there will be errors due to rounding and discretization. Over the years, new approaches to the FDM have been derived to improve the stability of the numerical solutions. These unique approaches are referred to as nonstandard finite difference methods (NFDM). The focus of this project will be to determine the effectiveness of two different NFDM proposed for an autonomous dynamical system and a class of reaction-diffusion equations. Effectiveness will be based on the accuracy of the exact solution and stability.
Title: Interpolation Methods (Mohammed Mutlaq Almatrafi, Mohamed Khalifa Aburakhis ECE, Independent Research)
Abstract: In this work, the interpolation methods, Polynomial interpolation, Cubic Splines interpolation, Akima cubic spline interpolation, Since function interpolation, and Radial Basis Function interpolation is implemented using MATLAB. The derivation and mathematical equations are presented. Finally, all methods are applied to one example for the sake of comparison. There is not enough literature on the comparison of interpolations methods, this work is an attempt to provide a survey of above methods.
Title: The comparison of FD and RBFs collocation methods for the solution of the heat equation (Lijun Lin, MATH) Abstract: The heat equation is widely used in various fields such as in industry and medicine for thermal treatment of the tumor. In this work, we are going to use two different numerical methods to solve the heat equation. It is known that Finite Difference (FD) and Radial Basis Functions (RBFs) collocation methods are both trustworthy for solving heat equation. To show the difference between the two methods, we would like to display the comparison by the final results, the error between approximate solution and exact solution, and other parameters in those methods.
4. Title: Runge-Kutta Methods to Explore Numerical Solutions of Reactor Point Kinetic Equations (Elizabeth N Boeke, MATH Capstone Project)
Abstract: This work is the study of Reactor Point Kinetic equations. This is a system of seven coupled ordinary differential equations, one for neutron density and six for delayed neutron precursors. The application of Runge-Kutta methods is used to study the system numerically. Solutions were then compared for different values of reactivity using MATLAB built-in functions ode23 and ode45. There are graphs and tables presented to compare these methods; theoretically, ode45 is of higher-order than ode23.
Students Research/Stander Symposium Posters (2017)
William Shovelton presented his work at the 13th Annual Dayton Engineering Sciences Symposium (DESS) undergraduate presentation competition held at Wright State University on October 23, 2017.
Title: A New Finite Difference Scheme to Study Reaction-Diffusion Models
Abstract: In this work, the applications and capabilities of a particular class of finite difference schemes will be discussed in relation to reaction-diffusion equations. This numerical method is beneficial because of the large number of nonlinear partial differential equations (NPDE) present in dynamical systems. For example, a reaction-diffusion equation can be used to model the laminar flame flow in combustion and other chemical and biological phenomenon. The particular scheme this work is concerned with is the positively preserving scheme. This method is applicable given that a relationship exists between time and space step-sizes and that initial data will always lead to positive values in future states. Reaction-diffusion equations with known exact solutions will be utilized to compare with the computational results.
2. How Mathematics Can Stop Crime
By William Shovelton
Abstract:
The Susceptible, Infected, and Recovered (SIR) Mathematical Model is widely used to study infectious diseases. Such models are also used to study predator-prey interactions, alcohol abuse, and social networks. Here, we will study a variation of SIR model for the interaction of police and gangs. In this work, we applied different numerical techniques to simulate the solution of the model, which is a system of coupled ordinary differential equations. This model was then manipulated to demonstrate the change in gang recruitment in correlation to the seasons.
3. Numerical Analysis of a Mathematical Model for the Formation of Alzheimer’s Disease
By Christopher Negri and Amelia Pompilio
Abstract:
Mathematics can be applied meaningfully to a variety of disciplines and research areas, especially the spread of diseases. The pathogenesis of Alzheimer’s disease remains largely ambiguous in current research because of the complex relationships between cell types due to aging. In this project, we perform a computational study of a mathematical model that is a system of coupled differential equations (DEs) to represent such relationships between cells. More specifically, the cells that will be analyzed are: amyloid-B(Ab), Microglia (state1&2) (M1) (M2), Neurons (Ns), Neuronaldebris(Nd), quiescentatrologia(Aq), astroglia proliferation(Ap).We use Runge-Kutta methods and Euler’s method to study the model.
Students Research/Stander Symposium Posters (2016)
A Mathematical Model for Alcoholism Epidemic (Independent Study Project)
By Marina Mancuso
Abstract:
Mathematical models are widely used to study the dynamics of infectious diseases as well as the social networks. This study considers a mathematical model for alcoholism transmission for a closed population. The model is derived from the SIR model for infectious diseases. The study utilizes the Runge-Kutta method as the numerical method to solve a system of differential equations describing the transmission of alcoholism.
Students Research/Stander Symposium Posters (2015)
1. Numerical Methods applied to an Enzyme Kinetics Model
Abstract:
In this work, we study enzyme kinetics using numerical techniques, such as Euler’s Method and Taylor’s Series Method. Our system consists of four ordinary differential equations, each of them describing the reaction rate of specific compounds in reaction. We represent the numerical solution and plots of each reactant. We compared the performance of our numerical methods with methods used in Callie Martins’ Enzyme Kinetics Spring 2012 Work.
2. A Mathematical Model for Enzyme Kinetics: Runge-Kutta Method
Abstract:
In this work we study a basic mathematical model for enzyme-substrate reaction. We summarize the enzyme kinetics model from J. D. Murray's Mathematical Biology book. We simplify the equations via nondimensionalization. Then we use the numerical solver called the Runge- Kutta methods to solve the system of differential equations describing the reaction.
3. Numerical Exploration of the Spread of Infectious Disease
Abstract:
This study will consider a model of SARS for a closed population. The mathematical model will be solved using numerical techniques and the solutions will be compared. It is assumed in this study that the incubation period is very short and individuals who recover from the disease become permanently immune.
Abstract:
Every animal’s temperature is directly correlated to the temperature of the environment that the animal lives in. The animal’s equilibrium temperature can be modeled using mathematical tools based on the temperature of the environment, the amount of solar radiation, and the heating characteristics of the specific animal. Newton’s Law of Cooling can be used to model this sort of phenomena of temperature changes. This mathematical model provides a relation between the unknown temperature and the derivative of this unknown temperature. In this work we will solve this model numerically using different techniques such as the Euler method, the three-term Taylor method, and the Runge-Kutta method. Using these three different mathematical methods, the animal’s body temperature due to the environment can be determined. We use Matlab for all numerical computations.
Abstract:
Mathematics is used in almost every area of life. With the development of modern computers, mathematical modelling and numerical simulation is new synergy in scientific discovery. In this work nonlinear equations are solved in order to determine the time of death to solve a crime. The equations are solved with few methods and we compare the accuracy of methods.
6. Using Differential Equations to model RLC Circuit
Abstract:
The center piece of our solar system is a burning ball of energy that has the power, in just one hour, to beam enough energy to the surface of earth to meet the entire energy needs of the planet for an entire year. Scientist are constantly trying to improve the efficiency of harnessing this energy through photovoltaic panels. These panels can be better modelled using RLC Circuit analysis and the use of differential equations. The use of differential equations allows for a better comprehension and quicker analysis of the given circuit.
7. Numerical Solution of Point Kinetic Equations for Nuclear Reactor
By Alexander Scholtes, Patrick Bruneel, Ryan Green
Abstract:
In this work, we will solve nuclear reactor point-kinematic equations. There are many numerical techniques to solve these models. We will solve this coupled system of differential equations using the simplest methods, such as the Taylor Series, Euler, and Runge Kutta methods using MatLab program. We will then compare the accuracy of each method.
8. A Mathematical Study of Hormone-induced Oscillations in Liver Cells
By Diqian Ren
Abstract:
Hormone-induced oscillations of the free intracellular calcium concentration are affected by hormone signals. In this paper, the tests and simulations use liver cells as a sample. This article introduce a mathematical model of Ca2+ hepatocytes oscillations, and then compare its predictions to the biochemical evidence. After analyzing the tests results and the mathematical model, the study shows the agonist-induced Ca2+oscillations in hepatocytes characters. At the same time, it shows that the influence of the calmodulin inhibitors to the oscillations. In this work we study the qualitative behavior of a model from the work of Roland Somogyi and Jorg W. Stucki.
By Huachun Yu
Abstract:
In this work we consider a telegraphic equation with Neumann boundary conditions. We use a finite difference scheme to approximate the solution. We will discuss the truncation error, convergence and stability of our scheme. We also present the numerical simulations.
10. A Numerical Study of a Mathematical Model of Cell Growth in Scaffolds
Abstract:
In this work we consider a mathematical model of cell growth in scaffolds for tissue regeneration. This model is taken from the work by Darae Jeong, Any Yum and Junseok Kim. We present numerical solutions of this system of coupled partial differential equations. We solve the system numerically using two different methods including finite difference methods, which is a classical method for solving partial differential equations. After the algorithms are developed they will be run and tested through a series of computer simulations that will provide evidence to which method is better in terms of accuracy and efficiency. Which will allow us to choose the better method.
Students Research/Stander Symposium Posters (2014)
1. Truncation Error for a Finite Difference Scheme for the Black-Scholes Model
Student - Lawrence M Kondowe
Finite difference methods are simplest and oldest methods among all the numerical techniques to approximate the solution of partial differential equations (PDEs). The derivatives in the partial differential equation are approximated by finite difference formulas. The error between the numerical solution and the exact solution is determined by the error between a differential operator to a difference operator. This error is called the discretization error or truncation error. The term truncation error reflects the fact that a finite part of a Taylor series is used in the approximation. In this work we will analyze the truncation error for a finite difference scheme for the Black Scholes PDE for the valuation of an option
2. Valuation of Options Using a Sinc Collocation Methods
Student - Elhusain S Saad
In this work we use a Sinc-Collocation method for the valuation of the European options. We use the famous Black-Scholes partial differential equation model of option valuation. We expand the function and its spatial derivatives using a cardinal expansion of Sinc functions. For time derivative we apply the finite difference method. Solutions are compared with the exact solutions.
Students Research/Stander Symposium Posters (2013)
Student - Nicholas Haynes
We demonstrate numerically the eventual time-periodicity of the solutions of the Korteweg-de Vries equation with periodic forcing at the boundary using the sinc-collocation method. This method approximates the space dimension of the solution with a cardinal expansion of sinc functions, thus allowing the avoidance of a costly finite difference grid for a third-order boundary value problem. The first-order time derivative is approximated with a weighted finite difference method. The sinc-collocation method was found to be more robust and more efficient than other numerical schemes when applied to this problem
2. Simulation of Nonlinear Waves Using Sinc Collocation-Interpolation
Student - Eric A Gerwin, Jessica E Steve
In this project we explore the Sinc collocation method to solve an initial and boundary value problem of nonlinear wave equation. The Sinc collocation method is based upon interpolation technique, by discretizing the function and its spatial derivatives using linear combination of translated Sinc functions. Our project will focus on multiple boundary conditions such as the well known Dirichlet and Neumann conditions. Our project will also focus on two established nonlinear partial differential equations: the Sine-Gordon equation and the Kortweg-de Vries equation.
3. Exploring the Sinc-Collocation Method for Solving the Integro-Differential Equation
Student - Han Li
In this project we study the Sinc approximation method to solve a family of integral differential equations. First we will apply the Sinc-collocation method to solve the second order Fredholm integro-differential equation. Numerical results and examples demonstrate the reliability and efficiency of this method. Secondly, various types of integro-differential equations are solved by Sinc-collocation technique and the numerical results are compared, to explore the stability of this method.
Students Research/Stander Symposium Posters (2012)
Student - Nicholas Haynes
A recent paper in the Journal of General Physiology disproved the hypothesis that the ciliary axoneme and the basal bodies of cilia impose selective barriers to the movement of proteins into and out of the the cilium using a combination of numerical modeling and observation with confocal and multiphoton microscopy. We compare the accuracy and computational efficiency of the numerical method used in the paper, known as the method of lines, to another method, known as sinc collocation, and discuss the possible use of other methods for improving the algorithm.
2. Stability Analysis of a Model for In Vitro Inhibition of Cancer Cell Mutation
Student - Chris Yakopcic
Human homeostasis is the body's ability to physiologically regulate its inner environment to ensure its stability in response to changes in the outside environment. An inability to maintain homeostasis may lead to death or disease, which is caused by a condition known as homeostatic imbalance. Normal cells follow the homeostasis when they proliferate and cancer cells do not. This work describes a model consisting of three reaction-diffusion equations representing in vitro interaction between two drugs. One inhibits proliferation of cancerous cells, and the other destroys these cells. A stability analysis of the model is performed with and without diffusion applied to the model. MATLAB is used to perform the stability analysis of the model.
3. Numerical Investigation into a Computational Approximation of Bifurcation Curves
Student - Joshua R Craven
In this project, I use computational tools to study the bifurcations in nonlinear oscillators. Matlab is first used to determine the slow flow phase portrait of each region and the characteristics of each critical point. Next, the parameters are discretized and for each set of values we find the locations of the real critical points and the eigenvalues of the Jacobian matrix. With this knowledge, we can approximate the bifurcation diagram. These results are compared with results from preexisting software.
Student - Alyssa C Lesko
IL-2 treatments have recently been identified to significantly reduce metastatic melanoma tumors and in some cases eliminate them. The problem with these treatments is that a set plan of administration varies from patient to patient and methods for determining treatment steps are still in the process of being developed. Previous research by Asad Usman and colleagues has used a numerical technique using MATLAB to decide treatment protocols. This research used the MATLABâ??s built in ode15 function to addresses treatment procedures including the starting and stopping of each treatment and the period in between each treatment. Building on this data and existing model, my project will explore several other numerical techniques such as ode23 and ode45 solvers, Eulerâ??s method, and the predictor corrector method to study IL-2 treatments in metastatic melanoma patients. A comparison will be made using error plots and tables, and a stability analysis using pplane7 will be investigated.
5. Mathematical Study of the Foot and Mouth Outbreak Model
Student - Jungmi Johnson
The foot and mouth outbreak in the UK in 2001 was a disastrous event for the country and the economic. The disease did not only cost UK government so much money to stop the disease, but it also affected the tourism industry. Mathematical epidemic models can provide clear strategy for minimizing the effect of such a disease, determining the expected manner of its progression in the event of a future outbreak based upon the latest available data on the epidemic. This project is to explore how to minimize the cost, how to contain the disease in minimal time, and how realistic these models will be considering the limitation of the model. Numerical and qualitative tools such as MATLAB's built in ode solver will be used.
6. Applying Mathematical Epidemic Modeling to Discover Commercially Beneficial Outbreak Control Methods
Student - Michael Ciesa
This project is a mathematical analysis and computational study of the 2001 foot and mouth epidemic in the UK. This model includes an application of the SIR model, developed by W. O. Kermack and A. G. McKendrick, with two additional factors: vaccination and incubation period infectives. The incubation period infectives represent the population of individuals infected with the disease that do not show symptoms, but still have the possibility of infecting other individuals.
7. Qualitative Study of an SIR epidemic model with an asymptotically homogeneous transmission function
Student - Karoline E. Hoffman
I will be exploring and analyzing an SIR epidemic model. This particular model has an asymptotically homogeneous transmission function which means the transmission rate is proportional to the fraction of the number of infective individuals to the total population. I will also look at a qualitative analysis of the model and then discuss the implications of the results of the model.
Students Research/Stander Symposium Posters (2011)
A Numerical Study of In Vitro Inhibition of Mutation of Cancer Cells Using Two Different Methods
Student - Giacomo Flora
The growth of in-vitro cancer cells has been studied using two numerical methods: the Predictor-Corrector and the Operator Splitting method. The mathematical model developed by Dey (2000) is used, which consists of three reaction-diffusion equations representing in vitro interaction between two drugs, one which inhibits the proliferation of the cancer cells and the other which destroy these cells. The solutions resulting from the application of the two methods are in excellent agreement. In addition stability analyses of model and diffusion free case have been performed.
Students Research/Stander Symposium Posters (2010)
1. A Graphical User Interface for Solving the Falkner-Skan Equation (Download all MATLAB codes here)
Student - Giacomo Flora
A Graphical User Interface (GUI) has been developed to solve the Falkner-Skan equation. This famous nonlinear third order Falkner-Skan equation on infinite interval describes several fluid dynamic problems under varying the value of two constant coefficients. The developed GUI enables the user to input these two coefficients, which will characterize the behavior of the corresponding solution, and the parameters necessary for the iterative methods used to solve the equation. At this regard, a shooting method developed by Zhang J. and Chen B. has been adopted. The required parameters for the numerical solution are represented by the initial shooting angle, the initial free boundary and two tolerance criteria.
Student - Elham Negahdary
In this work we revisit some relatively new techniques based on radial basis functions (RBFs) to interpolate, boundary-value and initial-boundary-value problems with high degrees of localization in space and/or time. First, we generate an initial discretization using equally spaced points and find the RBF approximation of the function. Next, we compute the interpolation error at points halfway between the nodes. Points at which the error exceeds a threshold become centers, and centers that lie between two points with error less than a smaller threshold are removed. The two end points are always left intact. We also adapt the shape parameters of RBFs based on the node spacing to prevent the growth of the conditioning of the interpolation matrix. The shape parameter of each center is chosen based on the spacing with nearest neighbors, and the RBF approximation is recomputed using the new center set. Recent work in the literature on radial basis functions method has shown some promising results in terms of accuracy and efficiency to solve higher order nonlinear partial differential equations. Since radial basis functions methods are completely meshfree, requiring only interpolation nodes and a set of points called centers defining the radial basis functions. Adaptive radial basis function approach is based on refining and coarsening nodes based on shape parameter, interpolation error and condition number of the interpolation matrix.
3. Kinetic Modeling of A Spherical Catalytic Particle
Student - Fadhel Zammouri
It is critical for chemical engineers to understand the kinetics behavior associated with catalytic particles. This is crucial in the design and fabrication of catalytic reactors. In this work, a mathematical model for the interplay between the rates of molecular transport (diffusion) and the intrinsic activity (chemical kinetics) is studied. The concept of effectiveness factor in catalytic first order chemical reactions, exothermic and endothermic, is addressed in detail. Also the behavior of chemical reaction rates and the temperature gradient in the catalytic particle with respect to stability is discussed. The Numerical solution of the model has been computed for various values of the parameters. For all of our computations and numerical simulations we have used MATLAB.
4. Measles Epidemic: Studying the Spread Using Numerical Techniques
Student - Jaye S. Flavin
Studying past epidemics is a necessary step in understanding and preventing the spread of future contagions. The measles epidemic in New York in the mid-1960s is an ideal case study for mathematical epidemiology because of the detailed records kept on those infected and the unique properties of measles as a disease. Using a Computer Algebra System (CAS), we will revisit the qualitative properties of the measles epidemic model and compare solutions using different numerical techniques.
Undergraduate Research in Mathematical Biology
Advisors: Muhammad Usman, Ph.D,
Amit Singh, Ph.D (Department of Biology)
Students Research/Stander Symposium Posters (2010)
5. A Computational Study of the Fitzhugh-Nagumo Action Potential System
Student(s) - Joseph R Salomone, Anna M. Stcyr, Angela Q. Umstead
The most celebrated example of mathematical modeling is the Hodgkin-Huxley model of nerve physiology. Their experiments were carried out on a giant axon of a squid, which was large enough for the implantation of electrodes. The Hodgkin-Huxley mathematical model for nerve cell action potential is a system of four coupled ordinary differential equations. The Fitzhugh-Nagumo two-variable action potential system behaves qualitatively like the Hodgkin-Huxley space-clamped system. Being simpler by two variables, action potentials and other properties of the Hodgkin-Huxley model may be visualized as phase-plane plots. We use MATLAB to study the numerical solutions as well as the qualitative properties of the model.
6. Mathematical Modeling of H1N1 Flu
Student(s) - William E. Balbach Nathan B. Frantz Brett R. Mershman William T. Weger
Mathematical models have been used to understand the dynamics of infectious diseases and to predict the future epidemic or pandemics. In 2009, a new strain of the influenza A (H1N1) virus spread rapidly throughout the world. This “swine flu” as it is commonly known, increased to what is considered an epidemic in a matter of months. In order to understand the spread of this virus, and similar patterns in future outbreaks, we study a simplified SIR mathematical model to answer some epidemiological questions. We solve the model numerically and also study the qualitative properties of the model. It is important
to mention that a solution of a mathematical model is not necessarily a solution to the real problem, but a solution to a simplified idealization of the real world problem.
7. Mathematical Modelling of Infectious Diseases
Student(s) - Kevin M. George, Branden J. King
Study of infectious diseases has become more important with increased global connectivity and personal contact. The discovery of the microscope in the 17th century caused a revolution in biology by revealing otherwise invisible. Mathematics broadly interpreted is a more general non optical microscope. Mathematical model helps to understand dynamics of how they spread, how many people are infected, resist the infection, or recover. In this work we study infectious diseases models qualitatively. These mathematical models are solved numerically using MATLAB.
Students Research/Stander Symposium Posters (2009)
David Aaby (2009) (Currently a graduate student in Biostatistics at University of Michigan)
Undergraduate Research in Mathematical Biology: A comparative study of numerical methods for the Hodgkin-Huxley model of nerve cell action potential, (Citation)
Advisors: Muhammad Usman, (Mathematics), Amit Singh, (Biology)
Stander Symposium 2009 Poster Presentation
Graduate Student Math Clinic Research
Kaity Jones
Using Neural Networks to Evaluate Options (April 30, 2021)Wenfeng Wu
A Computational Study of Option Pricing Models. (December 5, 2019)
Lijun Lin
A Comparison of Numerical Solutions of Black-Scholes Model (April 11, 2019)
Abigail Kramer
Numerical Solution of Coupled Diffusion Systems for Spatial Pattern Formations (May 2019)
Ohio Supercomputer Center (OSC)
News Article: Experiential Learning (University of Dayton students gain hands-on experience with computing, research)
Zhaopu Teng
Numerical solution of 2D Vasicek PDE model (Dec. 06, 2018)
Maha Abdullah N Reshedi
A comparison of numerical and analytical solutions of differential equations and systems (Dec. 06, 2018)
Eman Alasaf
A nonlinear analysis of an oscillator equation with damping and external force using a perturbation method (Aug. 2017)
Walaa Alharbi
A numerical study of an option pricing model using Radial Basis Functions collocation method. (Dec. 2016)
James Stewart (2016)
Math Clinic: A Numerical Study of a Mathematical Model of Cell Growth in Scaffolds
Nicholas Haynes (2013) (Ph.D. Physics from Duke University)
Math Clinic: Numerical demonstration of time periodicity of the Korteweg-de Vries equation with periodic forcing
Stander Symposium 2012 Poster Presentation
Stander Symposium 2013 Poster Presentation
Arthur Zeyda (2012)
Math Clinic: Numerical Solution of the Black-Scholes-Merton PDE using Sinc-Collocation method.
Joshua Craven (2012)
Math Clinic: Numerical Method for Determining Bifurcation Curves
Miriam Poteet (2009) (Ph.D. from AFIT)
Math Clinic: Stability of steady state solutions of the forced Kuramoto-Sivashinky(KS) equation
Stander Symposium 2009 Poster Presentation