Open Access. Powered by Scholars. Published by Universities.®
Numerical Analysis and Computation Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Partial Differential Equations (6)
- Physics (3)
- Engineering (2)
- Mathematics (2)
- Non-linear Dynamics (2)
-
- Ordinary Differential Equations and Applied Dynamics (2)
- Quantum Physics (2)
- Analysis (1)
- Artificial Intelligence and Robotics (1)
- Biochemistry, Biophysics, and Structural Biology (1)
- Civil and Environmental Engineering (1)
- Computational Neuroscience (1)
- Computer Sciences (1)
- Dynamic Systems (1)
- Engineering Science and Materials (1)
- Fluid Dynamics (1)
- Life Sciences (1)
- Mechanics of Materials (1)
- Neuroscience and Neurobiology (1)
- Numerical Analysis and Scientific Computing (1)
- Other Applied Mathematics (1)
- Other Biochemistry, Biophysics, and Structural Biology (1)
- Social Statistics (1)
- Social and Behavioral Sciences (1)
- Institution
- Publication
- Publication Type
Articles 1 - 11 of 11
Full-Text Articles in Numerical Analysis and Computation
Modified Equations Of Conformal Symplectic Exponential Time Differencing Methods, Taylore M. Keesler
Modified Equations Of Conformal Symplectic Exponential Time Differencing Methods, Taylore M. Keesler
Honors Undergraduate Theses
Planetary orbits, pendulums, and hurricanes are everyday examples of nonlinear systems, often studied using differential equations. However, their exact solutions can not always be computed, and thus, we use numerical methods to approximate their solutions. Certain methods are better suited to preserve special properties of the system like energy and geometry. Through previous numerical simulations, a conformal symplectic method proves more effective in this preservation. To understand why, we find the modified equation of a nonlinear system with damping, which is a differential equation for which the numerical solution is exact. Through backward error analysis, we obtain these modified equations, …
An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, Vu Giang, Alex Gnech
An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, Vu Giang, Alex Gnech
OUR Journal: ODU Undergraduate Research Journal
The Time-Independent Schrödinger Equation is a linear elliptic PDE that describes quantum-mechanical systems. Its significance in the science of submicroscopic phenomena, particularly quantum mechanics, is as central as Newton’s laws of motion are to classical mechanics. This study uses various methods, including novel neural networks and finite difference schemes, to solve the one-dimensional two-body equation.
Analytical And Numerical Analysis Of The Sirs Model, Catherine Nguyen
Analytical And Numerical Analysis Of The Sirs Model, Catherine Nguyen
Departmental Honors & Graduate Capstone Projects
Mathematical models in epidemiology describe how diseases affect and spread within a population. By understanding the trends of a disease, more effective public health policies can be made. In this paper, the Susceptible-Infected-Recovered-Susceptible (SIRS) Model was examined analytically and numerically to compare with the data for Coronavirus Disease 2019 (COVID-19). Since the SIRS model is a complex model, analytical techniques were used to solve simplified versions of the SIRS model in order to understand general trends that occur. Then by Euler's Method, the Runge-Kutta Method, and the Predictor-Corrector Method, computational approximations were obtained to solve and plot the SIRS model. …
Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe
Master's Theses
In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …
Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt
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 …
The Exact Factorization Equations For One- And Two-Level Systems, Bart Rosenzweig
The Exact Factorization Equations For One- And Two-Level Systems, Bart Rosenzweig
Theses and Dissertations
Exact Factorization is a framework for studying quantum many-body problems. This decomposes the wavefunctions of such systems into conditional and marginal components. We derive corresponding evolution equations for molecular systems whose conditional electronic subsystems are described by one or two Born-Oppenheimer levels and develop a program for their mathematical study.
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova
Mathematics & Statistics ETDs
The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …
Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski
Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski
Publications
The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.
School Policy Evaluated With Time-Reversible Markov Chain, Trajan Murphy, Iddo Ben-Ari
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.
Enhancement Of Krylov Subspace Spectral Methods Through The Use Of The Residual, Haley Dozier
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. …
Computational Methods In Civil Engineering, Nir Krakauer
Computational Methods In Civil Engineering, Nir Krakauer
Open Educational Resources
No abstract provided.