NCHU Course Outline
Course Name (中) 偏微分方程之數值方法(3220)
(Eng.) Numerical Methods for Partial Differential Equations
Offering Dept Department of Applied Mathematics
Course Type Required Credits 3 Teacher TENG CHUN HAO
Department Department of Applied Mathematics / Undergraduate Language English Semester 2026-FALL
Course Description Many scientific problems are described by partial differential equations. However, the analytical solution of partial differential equations has its limitations, often only applicable to linear problems with constant coefficients, and cannot be applied to real scientific and engineering problems. Numerical methods for partial differential equations are an applied mathematical tools that utilize the theoretical results and numerical methods to construct discrete systems of equations that mimic the properties of the original equations. Through computer computations, approximate solutions to partial differential equations are obtained to compensate for the shortcomings of analytical methods.

許多的科學問題是以偏微分方程的形式來描述。但偏微分方程的解析解法卻有其侷限性，往往只能用於常係數線性問題，對於真實的科學和工程問題解析方法往往無法應用。偏微分方程數值方法是一門應用數學方法，其精神是運用偏微分方程的理論結果和數值方法，建構一離散但仿原方程式的性質的系統方程式，透過計算機執行，求偏微分方程的近似解，以彌補解析方法的不足。
Prerequisites
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
1. Understand the basic concepts of numerical partial differential equations and how to use numerical methods to design calculation formats and obtain approximate solutions to partial differential equations.

2. Have a foundation in studying advanced numerical partial differential equations.

3. Have the basic research ability to conduct relevant topics.

1.了解數值偏微分方程的基本概念和如何使用數值方法設計計算格式，求得偏微分方程的近似解。
2.具備修習高等數值偏微分方程的基礎。
3.具備進行相關專題的基本研究能力。
2.Professional Knowledge in Mathematical Analysis
4.Professional Knowledge in Scientific Computation
5.Professional Knowledge in Computer Science
30
35
35
topic Discussion / Production
Networking / Distance Education
Visit
Exercises
Discussion
Practicum
Lecturing
Written Presentation
Oral Presentation
Quiz
Assignment
Attendance
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 Course Introduction
Basic concepts of numerical partial differential equations
Week 2 Advection equaltions: Wellposed-ness
Week 3 Summation-by-parts methods for numerical partial differential equations
Week 4 Numerical schemes for advection equations: stability analysis
Week 5 Wave equations on a spherical surface
Grid construction: Cubed-sphere
Week 6 Numerical scheme for advcection equations on spherical surfaces (1)
Week 7 Numerical scheme for advcection equations on spherical surfaces (2)
Week 8 Numerical scheme for advcection equations on spherical surfaces (2)
Week 9 Mid-term: Presentation
Week 10 Shallow water equations on a sphere
Skew-symmetric form
Week 11 Numerical scheme for shallow water equations on spherical surfaces (1)
Scheme construction
Week 12 Numerical scheme for shallow water equations on spherical surfaces (2)
Validation
Week 13 Numerical scheme for shallow water equations on spherical surfaces (3)
Simulation of flow over an isolated mountain
Week 14 Numerical scheme for shallow water equations on spherical surfaces (4)
Simulation of other wave problems
Week 15 Final: presentation
Week 16 Self-study: studying journal papers
self-directed
learning		    02.Viewing multimedia materials related to industry and academia.
Evaluation
Attendence: 10%

Homework: 20%

Mid-term (30%): Presentation(10%) and written report(20%)

Final(40%): Presnetation (20%) and written report (20%)
Textbook & other References
NA
Teaching Aids & Teacher's Website
Lecture notes will be provided in the I-learning system
Office Hours
Mon. 15:00-16:00
Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day：None Printed Date, year/month/day：2026 / 8 / 24
The second-hand book website：http://www.myub.com.tw/