SES # | TOPICS | KEY DATES |
---|---|---|

1 | Fundamental concepts and examples | |

2 | Well-posedness and Fourier methods for linear initial value problems | |

3 | Laplace and Poisson equation | |

4 | Heat equation, transport equation, wave equation |
Problem set 1 out Project proposal due |

5 | General finite difference approach and Poisson equation | |

6 | Elliptic equations and errors, stability, Lax equivalence theorem | |

7 | Spectral methods |
Problem set 2 out Problem set 1 due |

8 | Fast Fourier transform (guest lecture by Stephen Johnson) | |

9 | Spectral methods | |

10 | Elliptic equations and linear systems | |

11 | Efficient methods for sparse linear systems: multigrid |
Problem set 3 out Problem set 2 due |

12 | Efficient methods for sparse linear systems: Krylov methods | |

13 | Ordinary differential equations | Midterm report |

14 | Stability for ODE and von Neumann stability analysis | |

15 | Advection equation and modified equation |
Problem set 4 out Problem set 3 due |

16 | Advection equation and ENO/WENO | |

17 | Conservation laws: theory | |

18 | Conservation laws: numerical methods | |

19 | Conservation laws: high resolution methods |
Problem set 5 out Problem set 4 due |

20 | Operator splitting, fractional steps | |

21 | Systems of IVP, wave equation, leapfrog, staggered grids | |

22 | Level set method | |

23 | Navier-Stokes equation: finite difference methods | |

24 | Navier-Stokes equation: pseudospectral methods | Problem set 5 due |

25 | Particle methods | |

26 | Project presentations | Final report |

## Calendar

Course Info

Topics

Learning Resource Types

*assignment*Problem Sets

*group_work*Projects with Examples

*notes*Lecture Notes