MATH 5940-0

Brief

We will introduce basic numerical methods for fundamental Partial Differential Equations, such as the Poisson equation, heat equation and the wave equation with application to some advanced topics such as the transport-diffusion equation and reaction-diffusion systems.

Description

Course keywords: finite difference method, Poisson equation, heat equation, wave equation, ordinary differential equations 一、課程說明(Course Description) 上課時間: W3W4W5 預備課程: One semester of undergraduate Numerical Analysis. 課程內容: We will introduce basic numerical methods for fundamental Partial Differential Equations, such as the Poisson equation, heat equation and the wave equation with application to some advanced topics such as the transport-diffusion equation and reaction-diffusion systems. We will talk about both implementation (know how) as well as the error analysis (know why) of various numerical methods. For programming purpose, most of the methods we introduce will be limited to finite difference methods, except in the 1D case the finite element methods will also be introduced. 二、指定用書(Text Books) Typed lecture notes will be distributed in class. 三、參考書籍(References) R. J. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations. John C. Strikwerda, Finite Difference Schemes and Partial Differential Equations. 四、教學方式(Teaching Method) Lectures and lab hours. 五、教學進度(Syllabus) Two-point boundary value problems. Stability and Error Analysis for Elliptic Equations. Fast Fourier Transform and application in PDE. Iterative Methods for Sparse Linear Systems. Initial Value Problems for ODE. Stability analysis (von Neumann analysis) for parabolic and hyperbolic PDEs. 六、成績考核(Evaluation) In addition to midterm and final exams, there will be several homework assignments including both analysis and programming. Students are required to be familiar with programming language such as FORTRAN, C/C++ (preferred) or other modern programming languages. 七、可連結之網頁位址 www.math.nthu.edu.tw/~wangwc/teaching/ 本課程無涉及AI使用

Timetable

Remarks

應數組常微分方程一與科學計算擇一必修。

Restrictions

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization