Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 714: Methods of Computational Mathematics I

Qin Li, Fall 2017:

Previous description:

Numerical Methods for Ordinary Differential Equations

  • Basic ODE Theory
  • Explicit and implicit methods, stability, Runge-Kutta and multistep methods, stiff problems

Finite Difference Methods for Elliptic Partial Differential Equations

  • Iterative methods for solving large linear systems

Finite Difference Methods for Parabolic Partial Differential Equations

  • Numerical differentiations
  • Consistency, stability and convergence
  • Multidimensional problems

Finite Difference Methods for Hyperbolic Partial Differential Equations

  • Linear hyperbolic equations and their numerical discretizations
  • Basic theory for nonlinear hyperbolic equations: shock formation, weak solution and entropy condition, Riemann problem
  • Shock capturing methods: Godnov and Roe methods, high resolution methods (TVD and ENO), kinetic and relaxation methods
  • Hamilton-Jacobi equations and the level set method for front propagation

Finite Volume Methods for Partial Differential Equations
Spectral Methods for Partial Differential Equations

  • Fast Fourier transform
  • Fourier spectral method, pseudospectral methods
an undergraduate course in PDEs (on the level of Haberman's book on ``Applied Partial Differential Equations'') an undergraduate course in numerical analysis (on the level of Burden and Faires's book on ``Numerical Analysis'') knowledge in a programming language (e.g., Fortran, C/C++, or Matlab)

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI  53706

(608) 263-3054

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