## MATH3240 Numerical Methods for Differential Equations, 2012-13

### Announcement

• (Jan 31) First assignment has been uploaded. Please note the due date and no late submission is accepted.
• (Feb 21) Second assignment has been uploaded. Please note the due date and no late submission is accepted.
• (Mar 07) Special review session: March 11, 6:30-7:30pm, LSB C1
• (Mar 11) Second assignment has been corrected and you can get back from assignment box. Solution has also been uploaded. [Download file]
• (Mar 11) Since the mid-term exam, there will be no tutorial class on Mar 13th.
• (Mar 29) Problem 2(a) of Assignment 3 is revised.
• (Apr 10) New due date of Assignment 3 is April 18
• (Apr 16) In question 3(d)(e) of assignment 3, "value of x(t) with respect to t" means the values of x(t) by the approximation .
You are NOT supposed to graph the exact solution x(t).
• (Apr 25) Assignment 3 has been corrected. You can get back your work from the assignment box.

### General Information

#### Lecturer

Eric Chung
Office: LSB 205    Tel: 3943 7972    Email:

#### Teaching Assistant

Mak Tsz Fan
Office: LSB 222B    Tel: 3943 7963    Email:
Liu Keji
Office: LSB 222C    Tel: 3943 8570    Email:

#### Time and Venue

Lecture: Wednesday 4:30-6:15 at LSB LT3 and Thursday 4:30-5:15 at LSB LT4
Tutorial: Wednesday 6:30-7:15 at LSB LT4

### Course Description

Overview:

This course is an introduction to numerical methods for differential equations. Differential equations are common mathematical models of many realistic applications from physics, biology, finance and engineering. In order to quantitatively study these problems, one needs to find the solutions of the differential equations under consideration. However, analytical solutions to these differential equations are typically very difficult to compute. It is therefore important to design some methods to obtain approximate solutions in an efficient way. The focus of this course is to present some basic numerical methods for solving differential equations. We will consider both ordinary and partial differential equations.

Requirement:

In addition to the derivation of the methods, we will also prove stability and convergence theorems. A solid background in analysis and differential equations (ODE and PDE) is thus a very important prerequisite for this course. Moreover, there are some computational assignments, and some knowledge in MATLAB or C is needed.

Outline:

1. One step methods for ODE

2. Runge-Kutta methods for ODE

3. Multi-step methods for ODE

4. Systems of ODEs

5. Stiff problems

6. Boundary value problems

7. Finite difference methods for parabolic PDEs

8. Finite element methods for elliptic PDEs

### Textbooks

• Numerical Mathematics and Computing, by Cheney and Kincaid. (7th Edition)

### References

• An Introduction to Numerical Analysis, by Suli and Mayers.

### Assessment Scheme

 Assignment 10% Mid-term (March 13) 35% Final Exam 55%