## COURSE DESCRIPTION

Syllabus

Basic
course policies including attendance and grief absence

Finite difference methods for time dependent problems:
accuracy and stability, wave equations, parabolic equations.

A brief introduction to finite element method.

Solving linear systems: iterative methods, conjugate gradients and multigrid.

**Prerequisites:** MA 511 and MA 514 (or similar ones)

**LECTURE NOTES** (updated on Mar 29)

**LECTURE NOTES**

**Reference Books **(for those with *, online access
available via Purdue Library)**: **

- Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems*
- John C. Strikwerda, Finite Difference Schemes and Partial Differential Equations*
- G. Strang, Computational Science and Engineering
- Trefethen and David Bau, Numerical Linear Algebra

- Gustafsson, Bertil; Kreiss, Heinz-Otto; Oliger, Joseph, Time Dependent Problems and Difference Methods
- U. M. Ascher; Linda Ruth Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
- Demmel, James W., Applied Numerical Linear Algebra*
- Y. Saad, Iterative Methods for Sparse Linear Systems*
- Lloyd N. Trefethen, Spectral Methods in MATLAB*

## Problem Sets

HOMEWORK
# 1 due on Feb 5 Poisson1D_Dirichlet.m
Poisson2D_Neumann.m

HOMEWORK#2 due on Feb 21 Kepler_reference_q.mat

Demo code to draw ODE
solver stability region

HOMEWORK#3 due on Mar 19

HOMEWORK#4 due on Mar 28

HOMEWORK#5 due on April 11

## Schedule

Note: The schedule is subject to change. Check back for changes and updates

Date | Topic |
---|---|

Jan 8 Tue |
Introduction. 1D Poisson Equation. |

Jan 10 Th |
2D Poisson Equation. |

Jan 15 Tue |
Introduction to ODE. |

Jan 17 Th |
ODE Solvers. |

Jan 22 Tue |
2D Poisson |

Jan 24 Th |
Fourier Transform |

Jan 29 Tue |
wellposedness |

Jan 31 Th |
wellposedness |

Feb 5 Tue |
ODE |

Feb 7 Th |
Runge-Kutta |

Feb 12 Tue |
Runge-Kutta; Multi-Step Method |

Feb 14 Th |
Multi-Step Method |

Feb 19 Tue |
wellposedness of hyperbolic equations |

Feb 21 Th |
definition of stability for time-dependent problems |

Feb 26 Tue |
HW Solutions |

Feb 28 Th |
linear time-dependent PDE |

Mar 5 Tue |
linear time-dependent PDE |

Mar 7 Th |
stability of leap-frog
schemes |

Mar 12 Tue |
No Class. Spring Vacation. |

Mar 14 Th |
No Class. Spring Vacation. |

Mar 19 Tue |
stability of hyperbolic systems |

Mar 21 Th |
Jacobi/Gauss Seidel/SOR iterations; Steepest Descent |

Mar 26 Tue |
Conjugate Gradient |

Mar 28 Th |
HW#4 Solutions |

Apr 2 Tue |
Preconditioned CG; Mutligrid v-cycle |

Apr 4 Th |
Mutligrid |

Apr 9 Tue |
Multigrid; Sobolev space |

Apr 11 Th |
Finite element method |

Apr 16 Tue |
Finite element method |

Apr 18 Th |
Finite element method |

Apr 23 Tue |
Review |

Apr 25 Tue |
Review |