Numerical Analysis of Singular Perturbations and Convection-Diffusion Equations

本课题研究奇摄动常微分方程和偏微分方程的数值分析。在这种情况下，标准的数值方法有困难。本项目的主要目标是开发用于构造和分析这些问题的高阶有限差分离散化的工具。所采用的方法将结合古典和现代的一致性、稳定性和规律性的概念。离散化方案的开发将使用一般有限差分框架，并将在现实的数值实验和严格的数学分析环境中进行。

This project is concerned with the numerical analysis of singularly perturbed ordinary and partial differential equations. Standard numerical approaches have difficulty in such situations. The main objective of this project is to develop tools for the construction and analysis of high order finite-difference discretizations for these problems. The methods employed will consist of a combination of classical and modern notions of consistency, stability, and regularity. The development of the discretization schemes will use a general finite-difference framework and will take place in an environment of realistic numerical experimentation and rigorous mathematical analysis.