Math 809


Curriculum Vitae
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Syllabus: Click here for details in a PDF file


Course: Math 809, Numerical Methods for Partial Differential Equations III, MWF 12:30pm MWF@ Journalism Bldg 0139


Texts: Numerical Methods for Conservation Laws. LeVeque

bulletTopics: derivation of conservation laws, weak solutions, viscosity solution, entropy condition, Riemann problem, numerical schemes: Godunov, Lax-Friedrich, Lax-Wendroff, ENO, etc
bulletOffice Hours: WF 10:30-11:30am @MW410 and by appointment
bulletGrading: HW(60%),class participation(10%),and final project(30%)
bullet Policy: Late Homework and project will be no credit.
bulletTentative Schedule: updated regularly


Monday Wednesday Friday
Mar 28

Introduction to Scalar Hyperbolic Equations:


Definition of hyperbolic equations


Mar 30

Linear Advection Equation,

Burger Equation,

Method of Characteristics

Domain of dependence

Range of Influence

Weak Solution


Apr 1

Numerical Method:

1st Order Upwind

Apr 4

Numerical Method:


2nd Upwind

for u_t+ a u_x = 0

ENO for u_t + a u_x = 0

Lax-Friedrich Scheme

Apr 6

Riemann Problem

Shock speed

Apr 8

Entropy Conditions for Discontinuity

Apr 11

Entropy Condition based on the spreading of characteristics


Apr 13

Manipulating Conservation Laws

Entropy Functions

Apr 15

Some Scalar Example:

Traffic Flow

Sound Speed

Apr 18

Two Phase Flow

Shallow Water Eqns


Apr 20

Numerical Method for Linear System Equations

Backward Euler, Lax-Friedrichs, Lax-Wendroff, and Upwind

Apr 22

Local Truncation Error


The Lax Equivalence Theorem


Apr 25

Conservative Methods for Nonlinear Problems

Apr 27


Apr 29

Discrete Conservation


May 2

The Lax-Wendroff Theorem

May 4

Godunov's Method

May 6

Discrete entropy condition


May 9


May 11

Total variation stability

May 13

l_1-contracting numerical methods

May 16

Monotone methods

May 18

Higher Order Scheme

May 20

flux limiter

May 23

2D simulation

May 25

slope limiter

May 27

slope limiter for nonlinear eqnation

May 30

Memorial Day: no class

Jun 1

Central Scheme and Spectral Difference

Jun 3

ENO, WENO, Spectral Volume, DG

Jun 6

Final Presentation: 11:30am-1:18pm

Final Exams week

Jun 8

Final Exams Week

Jun 10

Final Exams Week