Math 807


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Syllabus: Click here for details in a PDF file


Course: Math 807, Numerical Methods for Partial Differential Equations I, MWF 12:30pm @BE0134A


Texts: Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Second Edition

bulletTopics: finite difference method for parabolic, hyperbolic, and elliptic PDEs, convergence, stability and consistency
bulletOffice Hours: MW 1:30-2:30pm @MW410 and by appointment
bulletGrading: HW(35%),class participation(5%),midterm (25%) and final exam(35%)
bullet Policy: Late Homework and project will be no credit.
bulletTentative Schedule: updated regularly


Monday Wednesday Friday
Sept 22  Sept 24

Autumn Classes Begin

Introduction: finite difference methods for PDEs

Sept 26

An explicit method of solution for parabolic equation

Sept 29

PDE to ODEs (Method of Lines)

Stability, Consistency, and Convergence

Oct 1

Crank-Nicolson implicit method

Oct 2 EA295 2:30pm: Alexander Kurganov gives a talk in Applied Seminar

"Fast Explicit Operator Splitting Method for Convection-Dominated Problems"

Oct 3

Weighted Average Method

Oct 6

Boundary Condition and Gerschgorin's theorem on bounds for eigenvalues



Oct 8

Fourier Analysis and Von Neumann's method

Oct 10

No class today (meeting in Minneapolis)

Last day to drop without a "W"

Oct 13

Von Neumann Analysis on single step methods:

explicit, Crank-Nicolson

Oct 15

Von Neumann Analysis on multi-step methods:

leap-frog, Dufort-Frankel Method

Oct 17

Matrix method for multi-step methods


Oct 20

ADI method for higher dimensional heat equation



Oct 22

Operator Splitting method

Oct 24

Heat equation on circular domain

Oct 27

Miscellaneous methods for improving accuracy

Increase stencil points; generate higher order by using truncation error information

Oct 29

Miscellaneous methods for improving accuracy

Multi-step method to increase accuracy in time; Richardson's correction approach

Oct 31

Non-linear parabolic equations

Newton's method

Nov 3 HW3

Midterm: 12:30pm-1:18pm

Nov 5

discuss midterm solution

Non-linear parabolic equations

Richtmyer's linearization method

Nov 7

Richtmyer's linearization method, conti

Lee's method

Nov 10

finite difference method for elliptic equation

truncation error, order of accuracy

Nov 12

Two dimensional problem

Nov 14

Discrete Maximal Principle; Consistency, Stability, Convergence for Elliptic Problems

Nov 17

Iterative Methods for Solving large linear systems of algebraic equations

A necessary and sufficient condition for the convergence of iterative methods

Nov 19

Rate of Convergence

Nov 21

Methods for accelerating the convergence of iterative process

Nov 24

Optimum Acceleration parameter for the SOR method

Nov 26

Relationship between the eigenvalues of the Jacobi and SOR iteration matrices to a block tridiagonal coefficient matrix

Nov 28

No Classes

Dec 1 HW5

2 cyclic matrices

Dec 3iFinal Project

2 cyclic matrices thm applied to Poisson's equation

Dec 5

Fast solver for Poisson Equations

Dec 8

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

Dec 10

Dec 12