Ordinary Differential Equations and Applied Dynamics Commons^™

Use Of Cubic B-Spline In Approximating Solutions Of Boundary Value Problems, Maria Munguia, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

Here we investigate the use of cubic B-spline functions in solving boundary value problems. First, we derive the linear, quadratic, and cubic B-spline functions. Then we use the cubic B-spline functions to solve second order linear boundary value problems. We consider constant coefficient and variable coefficient cases with non-homogeneous boundary conditions for ordinary differential equations. We also use this numerical method for the space variable to obtain solutions for second order linear partial differential equations. Numerical results for various cases are presented and compared with exact solutions.

Development Of A Two-Fluid Drag Law For Clustered Particles Using Direct Numerical Simulation And Validation Through Experiments, Ahmadreza Abbasi Baharanchi

FIU Electronic Theses and Dissertations

This dissertation focused on development and utilization of numerical and experimental approaches to improve the CFD modeling of fluidization flow of cohesive micron size particles. The specific objectives of this research were: (1) Developing a cluster prediction mechanism applicable to Two-Fluid Modeling (TFM) of gas-solid systems (2) Developing more accurate drag models for Two-Fluid Modeling (TFM) of gas-solid fluidization flow with the presence of cohesive interparticle forces (3) using the developed model to explore the improvement of accuracy of TFM in simulation of fluidization flow of cohesive powders (4) Understanding the causes and influential factor which led to improvements and …

Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids, Yupeng Shu

University of New Orleans Theses and Dissertations

The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.

Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker

Electronic Theses and Dissertations

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, Drake Knapper

Georgia State Undergraduate Research Conference

No abstract provided.

On Combining Neighbouring Extremals With Control Parameterization, Chongyang Liu, Qun Lin, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider the neighbouring extremals for a class of optimal control problems with control constraints. We first solve the optimal control problem using control parameterization method to obtain the optimal open-loop control and the optimal reference state. Then, a neighbouring feedback control law is derived for small state perturbations caused by changes on reference state at switching times.

Inżynieria Chemiczna Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

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Tematyka Prac Doktorskich, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

A Class Of High-Order Runge-Kutta-Chebyshev Stability Polynomials, Stephen O'Sullivan

Articles

The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order N is presented. Roots of FRKC stability polynomials of degree L = MN are used to construct explicit schemes comprising L forward Euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to ~ L². The associated stability domain scales as M² along the real axis. Marginally stable real-valued points on the interior of the stability domain are removed via a prescribed damping procedure. By construction, FRKC schemes meet all linear order conditions; for nonlinear …

A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach

Electronic Theses and Dissertations

In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.