抛物型方程有限差分法的案例教学

Case teaching of finite difference method of parabolic equation

抛物型方程作为微分方程数值解课程中的典型方程之一,在科学研究和工业设计中具有广泛应用.对于求解该方程的有限差分法,在教学过程中融入具体案例有助于激发学生的学习兴趣,让原本抽象且枯燥的数值方法和理论分析更加直观、具象.在课程内容的基础上进行延伸和拓展,形成与科研相结合的教学案例,可以进一步升华课程内容,培养学生学以致用的能力.

Parabolic equation,as one of the typical equations in the course of numerical solution of differential equations,has been widely applied in scientific research and industrial design.For the finite difference method of solving this equation,incorporating specific cases in the teaching process is helpful to stimulate students′interest in learning,and make the originally abstract and boring numerical methods and theoretical analysis more intuitive and concrete.The extension and expansion based on the course content to form a teaching case combined with the scientific research can further sublimate the course content,and cultivate students′ability to apply what they have learned.