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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 31 - 60 of 63
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
(R1511) Numerical Solution Of Differential Difference Equations Having Boundary Layers At Both The Ends, Raghvendra Pratap Singh, Y. N. Reddy
(R1511) Numerical Solution Of Differential Difference Equations Having Boundary Layers At Both The Ends, Raghvendra Pratap Singh, Y. N. Reddy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, numerical solution of differential-difference equation having boundary layers at both ends is discussed. Using Taylor’s series, the given second order differential-difference equation is replaced by an asymptotically equivalent first order differential equation and solved by suitable choice of integrating factor and finite differences. The numerical results for several test examples are presented to demonstrate the applicability of the method.
Analysis Of Covid-19 And Vaccine Administration In Mississippi, Megan Sickinger
Analysis Of Covid-19 And Vaccine Administration In Mississippi, Megan Sickinger
Honors Theses
In this work, we develop a simple mathematical model to observe the spread of COVID-19 and vaccine administration in Mississippi. Based on the well-known Kermack-McKendrick Susceptible-Infected-Removed epidemiological model, the ASIRD−V model has eight ordinary differential equations that split infected populations and recovered populations into vaccinated and unvaccinated populations. After determining that the system is reliable for real-world applications, we investigate and determine the stability and equilibrium points of this system. The system is found to be disease-free when R0 < 1 and endemic when R0 > 1. We use MATLAB to numerically solve the system and optimize the model’s parameters over four short periods, two with the …
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Rose-Hulman Undergraduate Mathematics Journal
A system of first-order differential equations that arises in a model for the growth of microorganisms in a chemostat with Monod kinetics is studied. A new, semi-implicit numerical scheme is proposed to approximate solutions to the system. It is shown that the scheme is uniquely solvable and unconditionally stable, and further properties of the scheme are analyzed. The convergence rate of the numerical solution to the true solution of the system is given, and it is shown convergence of the numerical solutions to the true solutions is uniform over any interval [0, T ] for T > 0.
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Rose-Hulman Undergraduate Mathematics Journal
For the SCUDEM V 2020 virtual challenge, we received an outstanding distinction for modeling a bird perched on a bicycle wheel utilizing the appropriate physical equations of rotational motion. Our model includes both theoretical calculations and numerical results from applying the Heaviside function for the swing motion of the bird. We provide a discussion on: our model and its numerical results, the overall limitations and future work of the model we constructed, and the experience we had participating in SCUDEM V 2020.
Epidemiological Assessment Of Wolbachia-Based Biocontrol For Reduction Of Dengue Morbidity, Olga Vasilieva, Oscar E. Escobar, Hector J. Martinez, Pierre-Alexandre Bliman, Yves Dumont
Epidemiological Assessment Of Wolbachia-Based Biocontrol For Reduction Of Dengue Morbidity, Olga Vasilieva, Oscar E. Escobar, Hector J. Martinez, Pierre-Alexandre Bliman, Yves Dumont
Biology and Medicine Through Mathematics Conference
No abstract provided.
2d Spatio-Temporal Patterns In Coupled Phase Oscillators: Spiral Waves And Chimeras, Yujie Ding, Bard Ermentrout
2d Spatio-Temporal Patterns In Coupled Phase Oscillators: Spiral Waves And Chimeras, Yujie Ding, Bard Ermentrout
Biology and Medicine Through Mathematics Conference
No abstract provided.
Understanding Biofilm-Phage Interactions In Mathematical Framework, Blessing Emerenini
Understanding Biofilm-Phage Interactions In Mathematical Framework, Blessing Emerenini
Biology and Medicine Through Mathematics Conference
No abstract provided.
Optimal Intervention Strategies To Minimize Spread Of Infectious Diseases And Economic Impact On A Dynamic Small-World Network, Malindi Whyte, Danielle Dasilva
Optimal Intervention Strategies To Minimize Spread Of Infectious Diseases And Economic Impact On A Dynamic Small-World Network, Malindi Whyte, Danielle Dasilva
Biology and Medicine Through Mathematics Conference
No abstract provided.
A Triphasic Physiologically Based Pharmacokinetic Model Of Vitamin D3 And Metabolites In Vitamin D Insufficient Patients, Colton W. Sawyer, Stacey M. Tuey, Raymond E. West Iii, Thomas D. Nolin, Melanie S. Joy
A Triphasic Physiologically Based Pharmacokinetic Model Of Vitamin D3 And Metabolites In Vitamin D Insufficient Patients, Colton W. Sawyer, Stacey M. Tuey, Raymond E. West Iii, Thomas D. Nolin, Melanie S. Joy
Biology and Medicine Through Mathematics Conference
No abstract provided.
Mathematical Model Of Zika Epidemic In Colombia, Sethupathy Ganesan
Mathematical Model Of Zika Epidemic In Colombia, Sethupathy Ganesan
Biology and Medicine Through Mathematics Conference
No abstract provided.
Mathematical Model Of Immune-Inflammatory Response In Covid-19 Patients, Quiyana M. Murphy
Mathematical Model Of Immune-Inflammatory Response In Covid-19 Patients, Quiyana M. Murphy
Biology and Medicine Through Mathematics Conference
No abstract provided.
Modeling And Analysis Of Social Contagion In Overweight And Obesity Epidemic, Chathuri Edirisinghe Arachchige
Modeling And Analysis Of Social Contagion In Overweight And Obesity Epidemic, Chathuri Edirisinghe Arachchige
Biology and Medicine Through Mathematics Conference
No abstract provided.
Mathematical Modelling Of Oncolytic Virotherapy As A Cancer Treatment, Maila Hallare, Iordanka Panayotova
Mathematical Modelling Of Oncolytic Virotherapy As A Cancer Treatment, Maila Hallare, Iordanka Panayotova
Biology and Medicine Through Mathematics Conference
No abstract provided.
Thoracoabdominal Asynchrony In A Virtual Preterm Infant: Computational Modeling And Analysis, Richard R. Foster, Laura Ellwein Fix
Thoracoabdominal Asynchrony In A Virtual Preterm Infant: Computational Modeling And Analysis, Richard R. Foster, Laura Ellwein Fix
Biology and Medicine Through Mathematics Conference
No abstract provided.
Olfactory Bulb Processing Of Ortho Versus Retronasal Odors, Michelle F. Craft, Andrea Barreiro, Shree Gautam, Woodrow Shew, Cheng Ly
Olfactory Bulb Processing Of Ortho Versus Retronasal Odors, Michelle F. Craft, Andrea Barreiro, Shree Gautam, Woodrow Shew, Cheng Ly
Biology and Medicine Through Mathematics Conference
No abstract provided.
Inferring Dynamics Of Biological Systems, Tracey G. Oellerich
Inferring Dynamics Of Biological Systems, Tracey G. Oellerich
Biology and Medicine Through Mathematics Conference
No abstract provided.
The Effect Of Prep Uptake And Adherence On The Spread Of Hiv In The Presence Of Casual And Long-Term Partnerships, Sylvia J. Gutowska, Katharine Gurski, Kathleen Hoffman
The Effect Of Prep Uptake And Adherence On The Spread Of Hiv In The Presence Of Casual And Long-Term Partnerships, Sylvia J. Gutowska, Katharine Gurski, Kathleen Hoffman
Biology and Medicine Through Mathematics Conference
No abstract provided.
The Interplay Between Costly Reproduction And Unpredictable Environments Shapes The Stability Of Cooperative Breeding, Glenn Steven Young
The Interplay Between Costly Reproduction And Unpredictable Environments Shapes The Stability Of Cooperative Breeding, Glenn Steven Young
Biology and Medicine Through Mathematics Conference
No abstract provided.
A Novel Chebyshev Wavelet Method For Solving Fractional-Order Optimal Control Problems, Ghodsieh Ghanbari
A Novel Chebyshev Wavelet Method For Solving Fractional-Order Optimal Control Problems, Ghodsieh Ghanbari
Theses and Dissertations
This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison …
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
Theses and Dissertations
The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Spora: A Journal of Biomathematics
Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year-1 reduces hepatitis B by over 90%, …
Predicting Box Office Revenues Using Differential Equation Models, Brenden David
Predicting Box Office Revenues Using Differential Equation Models, Brenden David
Mathematics Senior Capstone Papers
The growing popularity of the internet has increased exponentially in the past few decades. This sudden increase in popularity allows for users to gain access to more information than was thought possible in the past, including access to box-office movie revenues of previously released movies. Since we now have access to thousands of movie’s box office revenues, we can analyze some sort of trend within specific genres of movies. With these trends we develop a differential equations model that will predict the box office revenues of a movie that is in its early stages of the box office. This model …
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Spora: A Journal of Biomathematics
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R0 to changes in sociological parameter values.
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes
CODEE Journal
Starting with a toy climate model from the literature, we employ a system of two nonlinear differential equations to model the reciprocal effects of the average temperature and the percentage of glacial volume on Earth. In the literature, this model is used to demonstrate the potential for a stable periodic orbit over a long time span in the form of an attracting limit cycle. In the roughly twenty five years since this model appeared in the literature, the effects of global warming and human-impacted climate change have become much more well known and apparent. We demonstrate modification of initial conditions …
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Spora: A Journal of Biomathematics
Radiation therapy remains as one of the main cancer treatment modalities. Typical regimens for radiotherapy comprise a constant dose administered on weekdays, and no radiation on weekends. In this paper, we examine adaptive dosages of radiation treatment strategies for heterogeneous tumors using a dynamical system model that consist of radiation-resistant and parental populations with unique interactive properties, namely, PC3 and DU145 prostate cancer cell lines. We show that stronger doses of radiation given in longer time intervals, while keeping the overall dosage the same, are effective in PC3 cell lines, but not in DU145 cell lines. In addition, we tested …
Numerical Treatment For Special Type Of Mixed Linear Delay Volterra Integro-Differential Equations, Atheer J. Kadhim
Numerical Treatment For Special Type Of Mixed Linear Delay Volterra Integro-Differential Equations, Atheer J. Kadhim
Emirates Journal for Engineering Research
The idea of research is a representation of the nonlinear pseudo-random generators using state-space equations that is not based on the usual description as shift register synthesis but in terms of matrices. Different types of nonlinear pseudo-random generators with their algorithms have been applied in order to investigate the output pseudo-random sequences. Moreover, two examples are given for conciliated the results of this representation.
Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan
Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan
CMC Senior Theses
When it comes to women in professional hierarchies, it is important to recognize the lack of representation at the higher levels. By modeling these situations we hope to draw attention to the issues currently plaguing professional atmospheres. In a paper by Clifton et. al. (2019), they model the fraction of women at any level in a professional hierarchy using the parameters of hiring gender bias and internal homophily on behalf of the applicant. This thesis will focus on a key theory in Clifton et. al.’s analysis and explain its role in the model, specifically bifrucation analysis. In order to analyze …
New Techniques In Celestial Mechanics, Ali Abdulrasool Abdulhussein
New Techniques In Celestial Mechanics, Ali Abdulrasool Abdulhussein
Graduate Theses, Dissertations, and Problem Reports (ETD)
It is shown that for the classical system of the N body problem ( Newtonian Motion), if the motion of the N particles starts from a planar initial motion at t=t_{0}, then the motion of the N particles continues to be planar for every t\in[t_{0},t_{1}], assuming that no collisions occur between the N particles. Same argument is shown about the linear motion, namely, for the classical system of the N body problem, if the motion of the N particles starts from a linear initial motion at t=t_{0}, then the motion of the N particles continues to be linear for every …
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Theses and Dissertations
Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …
The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood
The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood
Theses and Dissertations (Comprehensive)
The motion of objects in the sky has captured the attention of scientists and mathematicians since classical times. The problem of determining their motion has been dubbed the Kepler problem, and has since been generalized into an abstract problem of dynamical systems. In particular, the question of whether a classical system produces closed and bounded orbits is of importance even to modern mathematical physics, since these systems can often be analysed by hand. The aforementioned question was originally studied by Bertrand in the context of celestial mechanics, and is therefore referred to as the Bertrand problem. We investigate the qualitative …