Mathematical Sciences: Algebraic and Algorithmic Aspects of Differential Equations.

这个项目的中心是分析具有多项式系数的线性微分方程解的代数性质，并在此分析的基础上开发可用于构造改进内插方案的算法。特别是，主要研究人员将使用伽罗瓦群理论来求解特殊函数形式的线性微分方程组。他还将研究这些特殊函数的代数结构，以期改进有限项积分微分方程的算法。最后，他将利用微分方程代数论中的技术，开发稀疏多项式和有理函数的改进内插公式。

This project centers around an analysis of the algebraic properties of the solutions of linear differential equations with polynomial coefficients and the development of algorithms based upon this analysis that can be used to construct improved interpolation schemes. In particular, the principal investigator will use the theory of galois groups to solve linear differential equations in terms of special functions. He will study also the algebraic structure of these special functions with a view to improving algorithms for integration of the differential equation in finite terms. And finally he will employ techniques from the algebraic theory of differential equations to develop improved interpolation formulas for sparse polynomials and rational functions.