必修課程介紹

• 預備知識：Numerical analysis, differential equations
• 適合年級： 研究生
• 課程簡介：

介紹有限差分法應用於雙曲偏微分方程式與拋物偏微分方程式的數值求解。

• 課程大綱：

1. Lagrange and Fourier approximation
2. Numerical differentiation and numerical integration
3. Finite difference method for initial value problems (hyperbolic equations)
4. Finite difference method for boundary value problems (elliptic equations)
5. Finite difference method for initial boundary value problems (parabolic equations)
6. Analysis of finite difference methods: consistency, stability and Von Neumann analysis for multi-steps methods.
7. Introduction of the spectral method, finite element method and finite volume method
8. Numerical methods for solving the convection-diffusion equation, Maxwell equation and Navier-Stoke equation.

• 參考書目：

1. Randali LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, 2007.
2. Christian Grossmann, Hans-Gorg Roos and Martin Stynes, Numerical Treatment of Partial Differential Equations, Springer, 2007.
3. Stig Larsson and Vidar Thomee, Partial Differential Equations with Numerical Method. Springer, 2005