Numerical Differential Equations MAT 460 class projects: Mathematical Modeling and Numerical Simulation of Problems modeled by ODEs and PDEs

Numerical Differential Equations MAT 460 class projects: Mathematical Modeling and Numerical Simulation of Problems modeled by ODEs and PDEs

Faculty: Andrea Dziubek

Projects of problems which can be modeled by ordinary or simple (linear or nonlinear) partial differential equations, e.g. spring-mass systems, framework, heat conduction, Bernoulli beam, wave equation, chemical reactions, data, finance.

Course Objectives:

Numerical methods for:

  • the solution of linear equation systems (direct decomposition methods),
  • the solution of nonlinear equation systems,
  • polynomial interpolation,
  • differentiation and integration of functions,
  • discretization of ordinary and partial differential equations.

Learning how to:

  1. code most of these methods (in Python),
  2. compute the order of convergence of a method and the error between an analytic solution and the solution of the discretized problem,
  3. estimate the potential and limits of a method and how to choose an appropriate method for different types of real-world problems.

A Python crash course in the first two weeks of the semester is offered by the Learning Center and the College of Arts and Sciences.