中英文介绍： 《微分方程数值解》是信息与计算科学专业学生学习的一门重要专业核心课程，它在科学计算和工程技术领域也有着非常广泛的应用。本课程主要介绍微分方程数值解的基本概念、基本理论和基础算法，为今后进一步学习数值分析和科学计算获得必要的基础理论知识。 这门课程分为理论教学和课程实践，理论教学主要内容包括两个部分：第一部分介绍常微分方程的单步法和多步法，以及刚性常微分方程组的数值解，数值方法的相容性、稳定性和误差估计。第二部分介绍偏微分方程：椭圆型、抛物型和双曲型方程的基本差分离散方法，包括一维问题和二维问题的差分格式。课程实践以计算机辅助进行，解决简单的数学模型以及复杂的实际物理问题，采用案例教学方法，突出自主学习和自主实践，激发学生的学习主动性，唤醒学生学习的热情。 通过此门课程系统的学习，培养计算数学专业学生的抽象思维能力、逻辑推理能力、科学计算能力。使得学生了解数学的作用和解决实际问题的强大生命力。本课程注重培养学生的科学计算能力和解决实际问题的能力，培养学生从事科学研究的数学素养，为同学们未来的科学研究打下坚实的基础！ Numerical solution of differential equations is a fundamental course in numerical analysis, and it has broad applications in scientific computation, engineering science and et. al. The course will provide the basic concepts, theories and algorithms in numerical solution to differential equations, and these are the requisite for students to learn advanced numerical analysis and scientific computation. This course consists of theoretical teaching and curriculum experiment. The main content of theoretical teaching is divided into two parts. The first part is devoted to numerical solution of ordinary differential equations (ODEs), which includes one-step methods, multi-step methods, numerical methods for stiff systems of ODEs, consistency, stability and convergence. The second part is followed by difference methods for the partial differential equations, including elliptic, parabolic and hyperbolic partial differential equations in one-dimensional space and two-dimensional space. The curriculum experiment is carried out with computer assistance, solving simple mathematical models and complex physical problems. Case teaching method is adopted to highlight independent learning and independent practice. It can stimulate students' learning initiative and awaken students' enthusiasm for learning. Through the learning of this course, students majoring in computational mathematics are trained to have abstract thinking ability, logical reasoning ability and scientific computing ability. Enable students to understand the role of mathematics and solve practical problems. In this course, the instructor will cultivate students’ ability of scientific computing and solving practical problems, students' mathematical literacy in scientific research, and lay a solid foundation for students' future scientific research.