冯康先生指出:“数值格式应尽可能多地保持原问题的本质特征”是构造数值格式的基本原则.保持微分方程一个或多个几何代数结构特征的算法称为保结构算法.算法不仅需要考虑保持结构特征,还应简单、高效、实用.本项目拟探讨以下问题：. 研究确定性微分方程简单、高效、实用保结构算法的构造，构造保持多种结构特征的数值算法，含有依赖于初始值的参数.把它们用于电磁学等领域问题的数值模拟.. 把DG、WENO等适合计算间断问题的格式与保结构算法思想相结合，探讨间断问题具有保结构特征的高效实用的数值格式的构造，使保结构算法思想在间断问题中的应用取得突破.. 为带有噪声驱动或随机参数输入的随机微分方程构造高效、实用的保结构算法.对于这类问题，关键需要解决随机变量在概率空间中的有效取样和解关于随机变量的展开表示等问题，讨论算法在量子力学等领域的应用.

As is pointed out by Feng Kang:“The essential characters of the original problems should be preserved as much as possible” is one of the fundamental rules in designing numerical scheme. A numerical scheme is said to be structure- preserving if it preserves one or more geometric-algebraic characters of the original differential equations. It is full of significance to study this kind of algorithms for differential equations. Moreover, an excellent algorithm should be simple, efficient and practical in coding. This project is devoted to exploring the following issues:. It focuses on developing simple, efficient and practical structure-preserving algorithms for deterministic differential equations endowed with some structures. It discusses to design a numerical scheme with parameters depending on initial values which preserves multiple geometric-algebraic structures. They also will be employed to numerical simulation in electromagnetism.. It combines numerical methods for discontinuous problems such as DG method, WENO scheme with structure-preserving ideas. In this item, efficient and practical numerical schemes with the characters of structure-preserving algorithms will be investigated for discontinuous issues such that some breakthroughs will be made in this field.. Efficient and practical structure-preserving algorithms will be studied for stochastic differential equations driven by noise or by random input parameters. Some sampling methods and the expansion of solution with respect to random variables in probability space will be studied such that the resulting deterministic problems can be solved efficiently. Moreover, we will consider their application to quantum mechanics.