Mathematical Sciences: Algebraic and Algorithmic Aspects of Differential Equations.

这个项目的中心围绕着分析的代数 线性微分方程解的性质 多项式系数和算法的发展 在这种分析的基础上，可以用来构建改进的 插值方案 特别是，首席研究员 我将用伽罗瓦群的理论来解线性微分 用特殊函数表示的方程。 他还将研究 这些特殊函数的代数结构， 微分方程积分的改进算法 in finite有限terms条款. 最后，他将运用 微分方程的代数理论发展改进 稀疏多项式和有理插值公式 功能协调发展的

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.