Math/CS 572: Numerical Mathematics II (Spring 2013)
 
Course Info: (syllabus)

 

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Prerequisite: Calculus, differential equation, linear algebra, some programming experience in FORTRAN, C, Matlab or a similar language.
 
Text:
  A first course in the numerical analysis of differential equations, by Arieh Iserles, 2nd Edition, Cambridge University Press, 2008.

Other reference : Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, by Randall J. LeVeque, SIAM, 2007.

Instructor: Dr. Yulong Xing                          Email: xingy (at) math.utk.edu
                Office: 214 Ayres Hall                 Office Hours: 10:30-11:30pm T, TH              
                Office Tel: (865) 974-4314

Class Meeting Times:  T, Th 12:40 - 1:55 PM,  Ayres Hall 112

Announcement

Week

M

T

W

R

F

01, Jan. 06.


 


First class (CANCELLED)


02, Jan. 13.


Newtons' method for system of nonlinear equations  

Secant method and unconstrained minimization

HW1


03, Jan. 20.

 

ODE background, Euler method

HW2

  TR, midpoint, and theta method.


04, Jan. 27.


Taylor method and numerical integration

HW3

  Explicit Runge-Kutta method


05, Feb. 03.


Explicit, Implicit Runge-Kutta, collocation method

HW4

Quiz 1

  Collocation method, Multistep method, accuracy


06, Feb. 10.


Multistep method, convergence and BDF method

HW5

  Stability and linear stability domain


07, Feb. 17.


A-stability, and stability of RK method

HW6

 

Stability of RK, multi-step methods

Programming assignment 1


08, Feb. 24.


No Class   No Class


09, Mar. 03.


Stability of multi-step method

Quiz 2

HW7

  PDE and finite difference operator


10, Mar. 10.


Finite different methods for 1D Poisson equation

 

  Midterm  

11, Mar. 17.

 

Finite difference methods for 2D Poisson equation

HW8

  Finite element methods for the Poisson equation  

12, Mar. 24.


Spring break   Spring break


13, Mar. 31.

 

Finite element methods for the Poisson equation: weak formulation

HW9

  Finite element methods for the Poisson equation: space, finite difference methods for the heat equation: A simple example  

14, Apr. 07.

 

Finite difference methods for the heat equation: method of line, stability

HW10

Solution to problem 3

 

Finite difference methods for the heat equation: stability

Programming assignment 2

 

15, Apr. 14.

 

Finite difference methods for the heat equation: multi-dimensional case

HW11

Quiz 3

 

Finite difference methods for the advection equation: method of line and some examples

 

16, Apr. 21.

 

Finite difference methods for the advection equation: stability

HW12

 

Last class

Finite difference methods for the advection equation: CFL condition, system

 

17, Apr. 28.


 


 


18, May. 05.

Final exam