Computer experiments with diffusion:finite differences, round-off error and animal stripes?

摘要

This paper describes a module for the teaching of diffusion to mechanical engineering students that can be part of a course on numerical methods or advanced engineering mathematics and as a precursor to a heat transfer course. The purpose of the module is to pull together many of the mathematical concepts in the early education of mechanical engineering students while at the same time introducing them to other important topics - an application of finite differences to the numerical approximation of partial differential equations, the importance of controlling round-off error in computational algorithms, and the time complexity of some numerical models. Students learn these topics through the execution of computer experiments. The first set of experiments cover the numerical approximation of heat conduction in a ring, and a second set cover the numerical approximation of the reaction and diffusion of chemicals that will produce the markings on an animal's tail. The learning outcomes of the module are evaluated with data from pre- and post-module surveys given to mechanical engineering students in several sections of a required course in numerical methods.