Term Project

Suggested Topics

Students can write on any topic they choose, but the topic must be approved by the instructor. You are NOT limited to the following topics; topics related to a student's research interest/area are especially encouraged.
  • Continuation methods
  • Delay differential equations
  • Differential algebraic equations
  • The Butcher theory
  • Gaussian quadrature and numerical ODEs
  • Numerical Methods for Boundary Value Problems
  • Differential equations in Biochemical Kinetics
  • Analysis of the Fitzhugh-Nagumo equations
  • Periodic solutions in systems of differential equations
  • Methods for stiff problems
  • Analysis of the Hodgkin-Huxley equations
  • Numerical methods for Reaction-Diffusion Equations
  • Numerical methods for Partial Differential Equations
  • Survey of numerical codes for differential equations
  • Finite element methods
  • Numerical methods in fluid dynamics
  • Solving hyperbolic equations
  • Methods for solving Poisson's equation
  • Multigrid methods
  • Homotopy
  • Numerical analysis of bifurcations
  • Numerical methods in (application)
  • Numerical Analysis of (a particular equation/system of equations)
  • Stability of methods for delay equations
  • Numerical solution of stochastic diffrential equations

Tentative Schedule

    Project parts must be turned in electronically, as an editable file, in one of the following formats: Latex (.tex); Rich-text (.rtf); a Mathematica notebook (.nb); Open-Office document (.ods); or Word document (.doc). Other formats such as Word-Perfect or Scientfic Notebook are not acceptable. Free versions of Latex and open office with equation editor are widely available on the internet for most operating systems. All equations must be embedded in the document in an editable form (not as image files). If possible, the student should also turn in a pdf file of the document.

  • Feb 15 (Week 3): Topic, Abstract, and at least 5 references including three primary sources. Copies of primary sources should be turned in as well (if you don't have pdf files you can turn in paper copies in class).
  • Mar 29 (Week 9): Paper Version 1 Due (I will suggest changes)
  • May 3 (Week 13): Paper Final Version Due
  • May 15, 17 (Week 15): Oral Presentations