Numerical Methods in Linear Algebra and Differential Equations
Mathematical models give us insights to better understand our world. However, the exact solutions to these models can often be difficult, and sometimes impossible, to obtain. In such instances, we rely on numerical algorithms that would give us approximate solutions. Due to the nature of approximations, we must also consider the accuracy and stability of the algorithms. Through this project, depending on interest and experience, students will:
- Implement standard algorithms to solve common problems in Linear Algebra, Ordinary Differential Equations, or Partial Differential Equations.
- Analyze the accuracy, stability, and efficiency of each algorithm.
- Attempt to improve standard algorithms (or invent new ones, if you’re feeling brave)
- Apply studied algorithms to solve more challenging mathematical models in Physics, Engineering, Finance, and/or Biology.
(Past projects include: Numerical Solutions to the Heat Equations, Schrödinger Equation, and Hodgkin-Huxley Model; Community-Detection Algorithms in Network Analysis)