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
	Topics: finite difference method for parabolic, hyperbolic, and elliptic PDEs, convergence, stability and consistency
	Office Hours: MW 1:30-2:30pm @MW410 and by appointment
	Grading: HW(35%),class participation(5%),midterm (25%) and final exam(35%)
	Policy: Late Homework and project will be no credit.
	Tentative 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 heat_eqn_explicit.m	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 HW1	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 HW2	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 HW4	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