I.The Basic Information of the Course
Course Number:202012420032
The EnglishName of theCourse：Numerical Methods for Partial Differential Equations
The ChineseName of theCourse：偏微分方程数值解法
In-classHours andAllocation(total class hours:32, classroom teaching:32classhours.)
Credit(s):2
Semester:2
AppliedDiscipline(ProfessionalDegreeCategory)：science and engineering majors
CourseObjectOriented：Masteranddoctoral student
EvaluationMode:Closed-bookExamination
TeachingMethod:MixedTeaching
CourseOpening Department:Collegeof Mathematical Sciences
II.Prerequisite Course
Mathematical analysis,Advanced algebra,Numerical calculation
III. The Objectives and Requirements of the Course
Through the study of this course, students can understand and master how to apply various methods of basic mathematics and computational mathematics to practical problems, research methods and derivation skills in application, as well as current hot issues and technical difficulties. To cultivate students' theoretical thinking ability and practical ability, to develop students' research ideas, and to lay a solid foundation for further applying mathematical knowledge to practical problems and engaging in mathematical applied research.
IV. The Content of the Course
Scientific computing is playing an increasingly important role in the natural sciences and science, technology and engineering sciences, and has become an indispensable tool in many important fields. The most important content of science and engineering calculation is to solve various partial differential equations or equations in scientific research and engineering technology. Numerical solution of partial differential equation usually requires regional subdivision of the definition domain of partial differential equation, discretization of partial differential equation, study of the morphology of discrete system (including the fitness and convergence of solutions, convergence speed), and finally calculation and solution of discrete system. Therefore, this course mainly introduces the modern numerical calculation methods often used to solve partial differential equations numerically, including:
1. Finite difference method: formation of discrete grids, treatment of boundary conditions, selection and analysis of discrete schemes, solution of linear equations and stability analysis.
2. Finite element method: includes the division of discrete elements, the construction of shape functions, the formation and solution of stiffness matrix, and the treatment of boundary conditions.
3. Finite volume method: formation of discrete grids, treatment of boundary conditions, selection and analysis of discrete formats, solution of linear equations and stability analysis.
4. Spectral methods: Including time-frequency domain conversion, integral transformation and discrete fast transformation.
V. Reference Books, Reference Literatures, and Reference Materials
1. Lu Jin-fu, Guan Zhi. Numerical solutions of partial differential equations (second edition). Higher Education Press, 2004.
2.Li Ronghua. Numerical solution of differential equation. Higher Education Press, 1996.
3. Li Likang et al. Numerical solution of differential equation. Fudan University Press, 1999.
4. Yu Dehao, etc. Numerical solution of differential equation. Science Press, 2003.
5. J.W.Thomas. Numerical Differential Equations. Springer-Verlag,1997.
6. Lu Jun An, Shang Tao. MATLAB solution of partial differential equation. Wuhan University Press, 2001
Outline Writer (Signature):冯国峰
Leader in charge of teaching at the College (Signature)：
Date：
中文
