科學計算   (88年度 下學期)

             N=新數館   Ns=新數館討論室   O=舊數館

* Time: Tues: 9:10-12:00 * Place: New Math Bldg. 102 * Instructor: Professor I-Liang Chern, chern@math.ntu.edu.tw * Aim: The goal of this course is to train students computational skills to tackle scientific problems. The main modeling tool is the partial differential equations. The numerical methods will include finite difference method, finite element method, probably spectral method, etc.~if time is allowed. Code design by using C++ or Fortran is required. I will cover the following topics: 1. Finite difference methods for parabolic equation — linear stability and accuracy analysis — energy method for stability analysis — Application to reaction-diffusion systems 2. Finite difference methods for hyperbolic equations — basic hyperbolic theory — upwinding methods, TVD methods, — flux-limiter, high-order Godunov methods, ENO schemes — Application to gas dynamics 3. Finite element method for elliptic equations — Finite element space, discrete Sobolev space — accuracy analysis — multigrid method — Application to Poisson equations 4. Numerical Linear Algebra — fast solvers for large linear systems * Prerequisite: some knowledge of partial differential equations, some basic knowledge on numerical analysis would be better

* Text books 1. John C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, California, U.S.A. 2. R. LeVeque, Numerical Methods for Conservation Laws, Birkhauser 3. Claes Johnson, Finite element method, Cambridge University Press

註：若大學部（大三以上）有興趣的話，可於加退選時辦理加選。