Math 481 – Numerical method for differential equations

Course Information

Class room and time:	Carver Hall 0098, TuTh 9:30 -10:50
Instructor Email and office number:	jyan@iastate.edu 294-8166
Office hour:	Tue & Thu 11-12pm or by appointment

Textbook:

· Numerical Analysis, by Richard L. Burden and J. Douglas Faires, 9^th edition. (Chapter 5)

· Numerical methods for ODE and PDE, notes by Wolfgang Kliemann. pdf

· Numerical mathematics, by Alfio Quarteroni, Riccardo Sacco and Fausto Saleri. (Texts in Applied Mathematics 37 by Springer-Verlag New York.)

Part 1 – ODE solvers: first order Euler method, high order Runge-Kutta method, multistep methods.

Part 2 – Finite difference method: local truncation error, stability, convergence. Numerical linear algebra.

Part 3 – Finite element method: numerical solution space, polynomial approximation, error estimate.

Home works and Exams:

Midterm is scheduled to be on MARCH 8^th? (in class)

Tentative Lectures Schedules:

Time Table	Covers	Lecture Notes
Week 1	ODE theory and Euler method	Lec 1 & 2
Week 2	Multi step method for ODE	Lec 3 & 4
Week 3	Error analysis and Runge-Kutta method	Lec 5 & 6
Week 4	Stability and convergence analysis-one step	Lec 7 & 8
Week 5	Stability Analysis-multi step, absolute stability	Lec 9 Lec 10
Week 6	Finite difference method for elliptic PDE	Lec 11 & 12
Week 7	Central difference central scheme, stability and convergence	Lec 13 & 14
Week 8	Variable coefficients and different boundary conditions	Lec 15 & 16
Week 9	Extension to multi-dimensional case	Midterm
Week 11	Finite difference for parabolic type equations	Lec 19 & 20
Week 12	Crank-Nicholson, backward Euler schemes	Lec 21 & 22
Week 13	Extension to 2D and introduction on finite element method	Lec 23 & 24
Week 14	Weak formulation and piecewise linear poly space	Lec 25 & 26
Week 15	Quadratic finite element and error analysis Extension to 2D and final discussion	Lec 27 & 28

Grading Policies:

Homework – 35%, Midterm exam – 30%, Final exam – 30%.

Letter grade: A’s group – above 85%, B’s group –above 70%, C’s group – below 70%.

Matlab Resources:(software, doc, lab)

Book: Introduction to scientific computing by Charles F.Van Loan

Lab: Carver hall 250, Carver hall 449 (hours)