Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Publication
- Publication Type
Articles 1 - 4 of 4
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Electronic Theses and Dissertations
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …
Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker
Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker
The Research and Scholarship Symposium (2013-2019)
Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Electronic Theses and Dissertations
Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …
Use Of Cubic B-Spline In Approximating Solutions Of Boundary Value Problems, Maria Munguia, Dambaru Bhatta
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.