Office: LSB 205 Tel: 3943 7972 Email:
|Mak Tsz Fan
Office: LSB 222B Tel: 3943 7963 Email:
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|
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.
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.
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
|Mid-term (March 13)||35%|
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