主讲人：Georgios Akrivis（约阿尼纳大学）

邀请人：李东方

课程时间：2021年10月28日（星期四）15:00-17:30

课程地点：Zoom ID: 981 2766 2356  Passcode: 780497

课程题目：Initial value problems

课程内容：1. Course Description: The initial value problem (IVP) for ordinary differential equations: Existence, uniqueness, and stability of solutions; examples of non-existence and non-uniqueness of solutions. Systems of linear differential equations. Numerical methods for initial value problems.

2. Learning Objectives: Understanding the basic facts for initial value problems. Understanding the fundamental qualitative characteristics of numerical methods for initial value problems, like stability, consistency, order of accuracy, and convergence. Familiarity with the main classes of numerical methods for initial value problems.

3. Expected Outcomes: After successful attendance of the course the students are expected to: Understand the basic facts for initial value problems. Understand the role of consistency, order of accuracy and stability (including A-stability, B-stability, and algebraic stability) of numerical methods for initial value problems. Know the main numerical methods for initial value problems. 

4. Literature and Study Materials:

（1）G. Akrivis: Numerical Methods for Initial Value Problems. Lecture Notes, 2021.

（2） D. F. Griffiths, D. J. Higham: Numerical Methods for Ordinary Differential Equations. Initial Value Problems. Springer–Verlag, Berlin, 2010.

（3）E. Hairer, Ch. Lubich, G. Wanner: Geometric Numerical Integration. Structure–Preserving Algorithms for Ordinary Differential Equations. 2nd ed., Springer–Verlag, Berlin, 2006.

个人简介：Georgios Akrivis希腊约阿尼拉大学教授，SIAM J Num. Anal 编委。计算数学顶级专家，主要研究微分方程数值解。在Numer Math, Math Comput, SIAM. J. Numer. Anal等杂志发表SCI论文50余篇。