Threshold of Collapse
School: Los Alamos High
Area of Science: Mathematics
Proposal: Our team’s plan for the 2011-2012 Supercomputing project is to conduct a study into the quantitative and qualitative behavior of dynamical systems. All of the dynamical systems we will study will be described by systems of ordinary differential equations (ODEs), which evolve in time. This study will focus on computing solutions to ODEs and studying the global properties of the solutions in phase space. The analysis of the qualitative properties of dynamical systems has applications in essentially all scientific fields. For our project, we will focus on dynamical systems that model economical and biomedical phenomena. Specifically, we will develop numerical solutions for differential equations that model nonlinear economic collapse and host/disease interactions. The strategy for working on this project will consist of developing a general numerical integrator in the C coding language and applying this numerical scheme to compute the solutions to the collapse and host/disease problems. A high-order Runge-Kutta-Fehlberg method will be applied to develop the numerical integration scheme. Example problems will be solved to validate and optimize the numerical performance of the integration scheme.
The final goal of our 2011-2012 Supercomputing project will be to perform parametric analyses of the collapse and host/disease problems to understand the global behavior of these problems in time. All work on this project will be done using Mac computers running the 10.6 operating system.
Sponsoring Teacher: Lee Goodwin
Mail the entire Team