MA/CS 615 - Numerical Methods for Partial Differential Equations

                     Spring 2019


Instructor: Xiangxiong Zhang

Office: MATH 406

Email: zhan1966@purdue.edu

Lectures: TR 3:00PM-4:15PM @ REC 113

Office Hours:  Wednesday 1:30-2:30 or by appointment



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)

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


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